The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 2, pp. 184-218.

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe the history of the development of geometric studies related to the work of the Moscow Mathematical Society from its early years to the present day. The main focus is on papers on “geometry in the large”.
@article{MMO_2016_77_2_a1,
     author = {I. Kh. Sabitov},
     title = {The {Moscow} {Mathematical} {Society} and metric geometry: from {Peterson} to contemporary research},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {184--218},
     publisher = {mathdoc},
     volume = {77},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2016_77_2_a1/}
}
TY  - JOUR
AU  - I. Kh. Sabitov
TI  - The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2016
SP  - 184
EP  - 218
VL  - 77
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MMO_2016_77_2_a1/
LA  - ru
ID  - MMO_2016_77_2_a1
ER  - 
%0 Journal Article
%A I. Kh. Sabitov
%T The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2016
%P 184-218
%V 77
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MMO_2016_77_2_a1/
%G ru
%F MMO_2016_77_2_a1
I. Kh. Sabitov. The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 2, pp. 184-218. http://geodesic.mathdoc.fr/item/MMO_2016_77_2_a1/

[1] Issledovaniya po metricheskoi teorii poverkhnostei, Novoe v zarubezhnoi nauke. Matematika, 18, Mir, M., 1980

[2] Vasilev A. M., Efimov N. V., Rashevskii P. K., “Issledovaniya po differentsialnoi geometrii v Moskovskom universitete v sovetskii period (k pyatidesyatiletiyu Sovetskoi vlasti)”, Vestnik MGU. Ser. Matem., mekh., 1967, no. 5, 12–23

[3] Matematika v SSSR za 40 let (1917–1957), v. 1, Obzornye doklady, GIFML, M., 1959 | MR | Zbl

[4] Rashevskii P. K., “Tenzornaya differentsialnaya geometriya”, Matematika v SSSR za 30 let, GITTL, M.–L., 1948, 283–918

[5] Evtushik L. E., Sabitov I. Kh., “Geometriya na kafedre matematicheskogo analiza”, Sovr. probl. matem. i mekh., 3:1 (2009), 42–45 | Zbl

[6] Geometriya i topologiya, Sovr. probl. matem. i mekh., 3, no. 2, 2009, 184 pp.

[7] “Sovetskaya matematika za 20 let”, UMN, 1938, no. 4, 3–13

[8] “O nauchnoi rabote nekotorykh otdelov Instituta matematiki MGU za 1936 g. Otdel teorii veroyatnostei i matematicheskoi statistiki. Otdel tenzornoi differentsialnoi geometrii”, UMN, 4 (1938), 289–294

[9] Matematika. Nauka v SSSR za pyatnadtsat let (1917–1932), GTTI, M., 1932

[10] Egorov D. F., “Uspekhi matematiki v SSSR”, Nauka i tekhnika v SSSR (1917–1927), v. 1, Rabotnik prosvescheniya, M., 1928, 223–234

[11] Lyusternik L. A., “«Matematicheskii sbornik»”, UMN, 1:1 (1946), 242–247

[12] Lapko A. F., Lyusternik L. A., “Iz istorii sovetskoi matematiki”, UMN, 22:6 (1967), 13–140 | Zbl

[13] Aleksandrov A. D., “Geometriya i topologiya v Sovetskom Soyuze”, UMN, 2:5 (1947), 9–92 | Zbl

[14] Euler L., Opera postuma, v. I, Petropoli, 1862, 494–495

[15] Legendre A.-M., Eléments de géométrie, Paris, 1794

[16] Cauchy A., “Sur les polygones et les polyèdres: second mémoire”, J. d'Ecole Polytechnique, IX:XVI (1813), 87–98

[17] L-v A., “O teorii parallelnykh linii N. I. Lobachevskogo”, Matem. sb., 3:2 (1868), 78–120

[18] Bertran Zh., “O summe uglov treugolnika”, Matem. sb., 4:4 (1870), 198–207

[19] Bunyakovskii V. Ya., “Zametka po voprosu o parallelnykh liniyakh”, Matem. sb., 6:1 (1872), 77–82

[20] Lakhtin L. K., “O zhizni i nauchnykh trudakh Nikolaya Ivanovicha Lobachevskogo (po povodu stoletnei godovschiny dnya ego rozhdeniya)”, Matem. sb., 17:3 (1894), 474–493

[21] Lakhtin L. K., “Ob odnom konkretnom istolkovanii planimetrii Lobachevskogo”, Matem. sb., 17:4 (1895), 767–790

[22] Klein F., “Ueber die sogenannte Nicht-Euklidische Geometrie”, Math. Ann., 4 (1871), 573–625 ; 253–303 | DOI | MR

[23] Riemann B., “Über die Hypothesen, welche der Geometrie zu Grunde liegen”, Gött. Abd., 13 (1868) ; 309–341 | MR

[24] A. P. Norden (red.), “Ob osnovaniyakh geometrii”, Sbornik klassicheskikh rabot po geometrii Lobachevskogo i razvitiyu ee idei, GITTL, M., 1956

[25] Bogomolov S. A., Vvedenie v neevklidovu geometriyu Rimana, ONTI GTTI, L.–M., 1934

[26] Peterson K. M., “Ob otnosheniyakh i srodstvakh mezhdu krivymi poverkhnostyami”, Matem. sb., 1:1 (1866), 391–438

[27] Bonnet O., “Mémoire sur la théorie des surfaces applicables sur une surface donnée. Première Partie”, J. d'Ecole Polytechnique, XXIV:41 (1865), 209–230; J. d'Ecole Polytechnique, XXV:42 (1867), 1–151

[28] Bobenko A. I., Exploring surfaces through methods from the theory of integrable systems. Lectures on the Bonnet Problem, SFB288 Preprint No 403, 1999 | MR

[29] Sabitov I. Kh., “Izometrichnye poverkhnosti s obschei srednei kriviznoi i problema par Bonne”, Matem. sb., 203:1 (2012), 115–158 | DOI | Zbl

[30] Peterson K. M., “Ob izgibanii poverkhnostei 2–go poryadka”, Matem. sb., 10:4 (1883), 476–523

[31] Mlodzeevskii B. K., “Karl Mikhailovich Peterson i ego geometricheskie raboty”, Matem. sb., 24:1 (1903), 1–21 | Zbl

[32] Cartan E., “Sur les couples de surfaces applicables avec conservation des courbures principales”, Bull. des Sciences Mathem., 66 (1942), 55–85 ; ØE uvres Complètes. Partie III, 2, 1591–1620 | MR

[33] Peterson K., Über Kurven und Flächen, M.–Leipzig, 1868

[34] Rossinskii S. D., “Karl Mikhailovich Peterson (1828–1881)”, UMN, 4:5 (1949), 3–13 | Zbl

[35] Egorov D. F., “K obschei teorii sootvetstviya poverkhnostei”, Matem. sb., 18:1 (1896), 86–107

[36] Mlodzeevskii B. K., “O poverkhnostyakh, svyazannykh s poverkhnostyami Petersona”, Matem. sb., 21:3 (1900), 450–460 | Zbl

[37] Mlodzeevskii B. K., “Ob izgibanii poverkhnostei Petersona”, Matem. sb., 24:3 (1900), 417–473

[38] Mlodzeevskii B. K., “Ob odnom preobrazovanii beskonechno–malykh izgibanii”, Matem. sb., 28:1 (1911), 205–214 | Zbl

[39] Egorov D. F., “Ob izgibanii na glavnom osnovanii pri odnom semeistve ploskikh ili konicheskikh linii”, Matem. sb., 28:1 (1911), 167–187 | Zbl

[40] Byushgens S. S., “Ob izgibanii poverkhnostei na glavnom osnovanii”, Matem. sb., 28:4 (1912), 507–528

[41] Finikov S. P., “Ob izgibanii poverkhnostei 2–go poryadka na glavnom osnovanii”, Matem. sb., 28:4 (1912), 529–543

[42] Byushgens S. S., “O tsiklicheskikh kongruentsiyakh i poverkhnostyakh Bianchi”, Matem. sb., 30:2 (1916), 296–313 | Zbl

[43] Finikov S. P., Obschaya zadacha izgibaniya na glavnom osnovanii, M., 1917

[44] Byushgens S. S., Izgibanie na glavnom osnovanii, M., 1918

[45] Egoroff D. Th., “Sur les surfaces, engendrées par la distrubution des lignes d'une famille donnée”, Matem. sb., 31:3 (1923), 153–184 | Zbl

[46] Finikoff S., “Sur les surfaces de M. Bianchi”, Matem. sb., 32:1 (1924), 249–254 | MR

[47] Finikov S. P., “Ob odnom sluchae osobogo izgibaniya kongruentsii”, Matem. sb., 32:1 (1924), 241–248

[48] Bucheguennce S., “Sur certaines familles invariables de courbes”, Matem. sb., 32:2 (1925), 348–352

[49] Maslov A. F., “O preobrazovanii Moutard'a i kvadratichnykh resheniyakh uravneniya s ravnymi invariantami”, Matem. sb., 32:3 (1925), 569–598 | Zbl

[50] Bucheguennce S., “Sur une class des hypersurfaces”, Matem. sb., 32:4 (1925), 625–631

[51] Bucheguennce S., “Sur les surfaces ayant une famille des parallèles planes ou sphériques”, Matem. sb., 32:4 (1925), 632–645

[52] Finikoff S., “Sur la déformation des surfaces à réseaux cinématiquemant conjugés persistant”, Matem. sb., 33:3 (1926), 129–160

[53] Masloff A. Th., “Sur la déformation des surfaces avec conservation d'un système conjugué”, Matem. sb., 33:1 (1926), 43–48 | Zbl

[54] Masloff A. Th., “Sur la déformation continue d'une classe des surfaces”, Matem. sb., 33:4 (1926), 367–370 | Zbl

[55] Finikoff S., “Sur la congruence rectiligne de roulement d'une infinité de manières”, Matem. sb., 34:1 (1927), 49–54

[56] Sretenskii L. N., “Ob izgibanii poverkhnostei”, Matem. sb., 36:2 (1929), 19–111 | Zbl

[57] Finikoff S., “Sur les quadriques de Lie et les congruences de M. Demoulin”, Matem. sb., 38:1–2 (1931), 48–97 | Zbl

[58] Finikov S. P., Teoriya kongruentsii, Gostekhizdat, M., 1950

[59] Finikov S. P., Teoriya par kongruentsii, Gostekhizdat, M., 1956

[60] Finikov S. P., Izgibanie na glavnom osnovanii i svyazannye s nim geometricheskie zadachi, Izd–vo ONTI NKTP SSSR, M.–L., 1937

[61] Delaunay N., “Sur les surfaces n'ayant qu'un coté et sur les points singuliers des courbes planes”, Bull. de la Soc. Math. de France, 26 (1898), 43–52 | DOI | MR | Zbl

[62] Lakhtin L. K., “Zametka ob odnostoronnikh poverkhnostyakh”, Matem. sb., 24:2 (1904), 178–193 | Zbl

[63] Mlodzeevskii B. K., “Issledovaniya ob izgibanii poverkhnostei”, Uchenye zapiski Moskovskogo universiteta. Otdel fiziko–matematicheskikh nauk, 1886, no. 7, 1–141

[64] Rashevskii P. K., Kurs differentsialnoi geometrii, GITTL, M., 1956

[65] Egorov D. F., “Boleslav Kornelievich Mlodzeevskii (Nekrolog)”, Matem. sb., 32:3 (1925), 449–452 | Zbl

[66] Rossinskii S. D., Boleslav Kornelievich Mlodzeevskii (1858–1923). Biograficheskii ocherk, Izd–vo MGU, M., 1950

[67] Bogachev V. I., “K istorii otkrytiya teorem Egorova i Luzina”, Istoriko–matematicheskie issledovaniya. Vtoraya seriya, 2009, no. 13(48), 54–67

[68] Egorov D. F., “Ob odnom klasse ortogonalnykh sistem”, Uchenye zapiski Moskovskogo universiteta, 1901, no. 18, 1–239

[69] Egorov D. F., Raboty po differentsialnoi geometrii, Nauka, M., 1970

[70] Darboux G., Leçons sur les systèmes orthogonaux et les coordonnées curvilignes, Paris, 1910 | MR

[71] Kuznetsov P. I., “Dmitrii Fedorovich Egorov (k 100–letiyu so dnya rozhdeniya)”, UMN, 26:5 (1971), 169–206 | Zbl

[72] Nikonov I. M., Fomenko A. T., Shafarevich A. I., “O rabotakh D. F. Egorova po differentsialnoi geometrii”, Istoriko–matematicheskie issledovaniya. Vtoraya seriya, 2009, no. 13(48), 49–53

[73] Kolyagin Yu. M., Savvina O. A., Dmitrii Fedorovich Egorov. Put uchenogo i khristianina, Izd–vo PSTGU, M., 2010

[74] Egorov D. Th., “Sur les systèmes orthogonaux admettant un groupe continu de transformations de Combescure”, C.R. Acad. Sci. Paris, CXXXI (24 Octobre 1900), 668; CXXXII (14 janvier 1901), 174 (обе работы опубликованы в русском переводе в [69])

[75] Dubrovin B. A., Novikov S. P., “Gamiltonov formalizm odnomernykh sistem gidrodinamicheskogo tipa i metod usredneniya Bogolyubova–Uizema”, DAN SSSR, 270:4 (1983), 781–785

[76] Tsarev S. P., “O skobkakh Puassona i odnomernykh gamiltonovykh sistemakh gidrodinamicheskogo tipa”, DAN SSSR, 282:3 (1985), 534–537 | Zbl

[77] Dubrovin B. A., Novikov S. P., “Gidrodinamika slabo deformirovannykh solitonnykh reshetok. Differentsialnaya geometriya i gamiltonova teoriya”, UMN, 44:6 (1989), 29–98 | Zbl

[78] Tsarev S. P., “Geometriya gamiltonovykh sistem. Obobschenyi metod godografa”, Izv. AN SSSR. Ser. Matem., 54:5 (1990), 1048–1068 | Zbl

[79] Mokhov O. I., Ferapontov E. V., “Nelokalnye gamiltonovy operatory gidrodinamicheskogo tipa, assotsiirovannye s metrikami postoyannoi krivizny”, UMN, 45:3 (1993), 191–192

[80] Ferapontov E. V., “Differentsialnaya geometriya nelokalnykh gamiltonovykh operatorov gidrodinamicheskogo tipa”, Funkts. analiz i ego pril., 25:3 (1991), 37–49 | Zbl

[81] Ferapontov E. V., “Gamiltonovy sistemy gidrodinamicheskogo tipa i ikh realizatsii na giperpoverkhnostyakh psevdoevklidova prostranstva”, Itogi nauki i tekhn. Ser. Problemy geometrii. Tr. geom. sem., 22, VINITI, M., 1990, 59–96 | Zbl

[82] Krichever I. M., “Algebro–geometricheskie $n$-ortogonalnye krivolineinye sistemy koordinat i resheniya uravnenii assotsiativnosti”, Funkts. analiz i ego pril., 31:1 (1997), 32–50 | DOI | Zbl

[83] Mokhov O. I., “Soglasovannye i pochti soglasovannye psevdorimanovy metriki”, Funkts. analiz i ego pril., 35:2 (2001), 24–36 | DOI | Zbl

[84] Pavlov M. V., Tsarev S. P., “Trigamiltonovy struktury egorovskikh sistem gidrodinamicheskogo tipa”, Funkts. analiz i ego pril., 37:1 (2003), 38–54 | DOI | Zbl

[85] Bukhshtaber V. M., Leikin D. V., Pavlov M. V., “Egorovskie gidrodinamicheskie tsepochki, uravnenie Shazi i gruppa $\mathrm{SL}(2,C)$”, Funkts. analiz i ego pril., 37:4 (2003), 13–26 | DOI | Zbl

[86] Zakharov V. E., “Description of the $n$-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. I: Integration of the Lame equations”, Duke Math. J., 94:1 (1998), 103–139 | DOI | MR | Zbl

[87] Finikov S. P., “Sergei Sergeevich Byushgens (k semidesyatiletiyu so dnya rozhdeniya)”, UMN, 8:4 (1953), 185–192 | Zbl

[88] Vasilev A. M., Laptev G. F., “Sergei Pavlovich Finikov. Nekrolog”, UMN, 19:4 (1964), 157–162

[89] Bazylev V. T., “K 90–letiyu so dnya rozhdeniya S. P. Finikova”, Itogi nauki i tekhn. Ser. Problemy geometrii. Tr. geom. sem., 6, VINITI, M., 1974, 17–24 | Zbl

[90] Burstin S., “Ein Beitrag zum Problem der Einbettung der Riemannschen Räume in euklidischen Räumen”, Matem. sb., 38:3–4 (1931), 74–85

[91] Burstin S., “Beiträge der Verbiegung von Hyperflächen in euklidischen Räumen”, Matem. sb., 38:3–4 (1931), 86–93

[92] Sabitov I. Kh., “K istorii odnoi interpretatsii izgibanii na glavnom osnovanii”, Istoriko–matematicheskie issledovaniya. Vtoraya seriya, 2000, no. 5(40), 164–166

[93] Kagan V. F., Osnovy teorii poverkhnostei, v. 2, OGIZ, GITTL, M.–L., 1948

[94] Luzin N. N., “Dokazatelstvo odnoi teoremy teorii izgibanii”, Izv. AN SSSR. Otdelenie tekhnicheskikh nauk, 1939, no. 2, 81–106; No 7, 115–132 ; No 10, 65–84 | Zbl

[95] Aleksandrov A. D., “O beskonechno malykh izgibaniyakh poverkhnostei”, Matem. sb., 1(43):3 (1936), 307–322

[96] Kon–Fossen S. E., “Izgibaemost poverkhnostei v tselom”, UMN, 1936, no. 1, 33–76 | Zbl

[97] Dorfman A. G., “Reshenie uravneniya izgibaniya dlya nekotorykh klassov poverkhnostei”, UMN, 12:2 (1957), 147–150

[98] Efimov N. V., “Izgibanie okrestnosti parabolicheskoi tochki poverkhnosti”, Matem. sb., 6(48):3 (1939), 427–474

[99] Efimov N. V., “Issledovanie izgibaniya poverkhnosti s tochkoi uploscheniya”, Matem. sb., 19(61):3 (1946), 461–488

[100] Efimov N. V., “Issledovanie deformatsii poverkhnosti, soderzhaschei tochku s nulevym znacheniem gaussovoi krivizny”, Matem. sb., 23(65):1 (1948), 89–125

[101] Efimov N. V., “Kachestvennye voprosy teorii deformatsii poverkhnostei «v malom»”, Tr. MIAN, 30, 1949, 3–128

[102] Efimov N. V., “Kachestvennye voprosy teorii deformatsii poverkhnostei”, UMN, 3:2 (1948), 47–158 | Zbl

[103] Efimov N. V., “O zhestkosti «v malom»”, DAN SSSR, 60:5 (1948), 761–764 | Zbl

[104] Entsiklopediya elementarnoi matematiki, v. 5, Geometriya, Nauka, M., 1966

[105] Alekseevskii D. V., Vinogradov A. M., Lychagin V. V., “Osnovnye idei i ponyatiya differentsialnoi geometrii”, Geometriya-1, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 28, VINITI, M., 1988, 5–289

[106] Alekseevskii D. V., Vinberg E. B., Solodovnikov A. S., “Geometriya prostranstv postoyannoi krivizny”, Geometriya-2, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 29, VINITI, M., 1988, 5–146

[107] Vinberg E. B., Shvartsman O. V., “Diskretnye gruppy dvizhenii prostranstv postoyannoi krivizny”, Geometriya-2., Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 29, VINITI, M., 1988, 147–259

[108] Burago Yu. D., “Geometriya poverkhnostei v evklidovykh prostranstvakh”, Geometriya-3, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 48, VINITI, M., 1989, 5–97

[109] Reshetnyak Yu. G., “Dvumernye mnogoobraziya ogranichennoi krivizny”, Geometriya-4, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 70, VINITI, M., 1989, 7–189

[110] Berestovskii V. N., Nikolaev I. G., “Mnogomernye obobschennye rimanovy prostranstva”, Geometriya-4, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 70, VINITI, M., 1989, 190–272 | Zbl

[111] Babenko I. K., “Zamknutye geodezicheskie, asimptoticheskie ob'emy i kharakteristiki gruppovogo rosta”, Izv. AN SSSR. Ser. Matem., 52:4 (1988), 675–711 | Zbl

[112] Babenko I. K., “Asimptoticheskie invarianty gladkikh mnogoobrazii”, Izv. AN SSSR. Ser. Matem., 56:4 (1992), 707–751 | Zbl

[113] Fomenko A. T., “Mnogomernaya problema Plato v rimanovykh mnogoobraziyakh”, Matem. sb., 89:3 (1972), 475–519

[114] Ivanov A. O., Tuzhilin A. A., “Odnomernaya problema Gromova o minimalnom zapolnenii”, Matem. sb., 203:5 (2012), 65–118 | DOI | Zbl

[115] Mokhov O. I., “Realizatsiya frobeniusovykh mnogoobrazii kak podmnogoobrazii v psevdoevklidovykh prostranstvakh”, Tr. MIAN, 267, 2009, 226–224

[116] Sabitov I. Kh., Shefel S. Z., “O svyazyakh mezhdu poryadkami gladkosti poverkhnosti i ee metriki”, Sib. matem. zhurn., 17:4 (1976), 916–925 | Zbl

[117] Gromov M. L., Rokhlin V. A., “Vlozheniya i pogruzheniya rimanovykh mnogoobrazii”, UMN, 25:5 (1970), 3–62

[118] Sabitov I. Kh., “Regulyarnost vypuklykh oblastei s regulyarnoi v klassakh Geldera metrikoi”, Sib. matem. zhurn., 17:4 (1976), 907–915 | Zbl

[119] Rozendorn E. R., “Nekotorye voprosy teorii otobrazhenii s prilozheniyami k issledovaniyu poverkhnostei otritsatelnoi krivizny pri ponizhennykh usloviyakh regulyarnosti”, Tr. MMO, 53, 1990, 171–191 | Zbl

[120] Sabitov I. Kh., “O zhestkosti gofrirovannykh poverkhnostei vrascheniya”, Matem. zametki, 14:4 (1973), 517–522 | Zbl

[121] Efimov N. V., Usmanov Z. D., “Beskonechno malye izgibaniya poverkhnostei s tochkoi uploscheniya”, DAN SSSR, 208:1 (1973), 28–31 | Zbl

[122] Sabitov I. Kh., “Lokalnaya teoriya izgibanii poverkhnostei”, Geometriya-3, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 48, VINITI, M., 1989, 196–270

[123] Klimentov S. B., Sabitov I. Kh., Usmanov Z. D., “Deformatsiya poverkhnostei «v malom»: ot N. V. Efimova do sovremennykh issledovanii”, K 100–letiyu so dnya rozhdeniya N. V. Efimova, v. VI, Sovremennye problemy matematiki i mekhaniki, 2, Matematika, Izd-vo MGU, M., 2011, 34–48 | Zbl

[124] Ivanova–Karatopraklieva I., Sabitov I. Kh., “Izgibanie poverkhnostei. I”, Itogi nauki i tekhn. Ser. Problemy geometrii. Tr. geom. sem., 23, VINITI, M., 1991, 131–184

[125] Sabitov I. Kh., “O svyazyakh mezhdu beskonechno malymi izgibaniyami raznykh poryadkov”, Ukr. geom. sb., 35 (1992), 118–124

[126] Poznyak E. G., “Primer zamknutoi s osoboi tochkoi poverkhnosti, imeyuschei schetnuyu fundamentalnuyu sistemu beskonechno malykh izgibanii”, UMN, 12:3 (1957), 363–367

[127] Poznyak E. G., “O nezhestkosti vtorogo poryadka”, UMN, 16:1 (1961), 157–161 | Zbl

[128] Sabitov I. Kh., “O beskonechno malykh izgibaniyakh zhelobov vrascheniya. I”, Matem. sb., 98:1 (1975), 113–129 ; “О бесконечно малых изгибаниях желобов вращения. II”, Матем. сб., 99:1 (1976), 49–57 | MR | Zbl

[129] Sabitov I. Kh., “Issledovanie zhestkosti i neizgibaemosti analiticheskikh poverkhnostei vrascheniya”, Vestnik MGU. Ser. Matem., mekh., 5 (1986), 29–36 | Zbl

[130] Sabitov I. Kh., “Zhestkost i neizgibaemost «v malom» i «v tselom» poverkhnostei vrascheniya s uploscheniyami v polyusakh”, Matem. sb., 204:10 (2013), 127–160 | DOI

[131] Sabitov I. Kh., “Beskonechno malye izgibaniya 2–go poryadka poverkhnostei vrascheniya s uploscheniyami v polyusakh”, Matem. sb., 205:12 (2014), 111–140 | DOI | Zbl

[132] Sabitov I. Kh., “Kvazikonformnye otobrazheniya poverkhnosti, porozhdennye ee izometricheskimi preobrazovaniyami, i izgibaniya poverkhnosti na sebya”, Fund. i prikl. matem., 1:1 (1995), 281–288 | Zbl

[133] Sabitov I. Kh., “Vozmozhnye obobscheniya lemmy Minagava–Rado o zhestkosti poverkhnosti vrascheniya s zakreplennoi parallelyu”, Matem. zametki, 19:1 (1976), 123–132

[134] Ivanova–Karatopraklieva I., Sabitov I. Kh., “Izgibanie poverkhnostei”, Itogi nauki i tekhn. Ser. Sovrem. matem. i ee pril. Tematicheskie obzory, 8, VINITI, M., 1995, 108–167

[135] Ivanova–Karatopraklieva I., Markov P. E., Sabitov I. Kh., “Izgibanie poverkhnostei. III”, Fund. i prikl. matem., 12:1 (2006), 3–57

[136] Efimov N. V., “Nevozmozhnost v trekhmernom evklidovom prostranstve polnoi regulyarnoi poverkhnosti s otritsatelnoi verkhnei granyu gaussovoi krivizny”, DAN SSSR, 150:6 (1963), 1206–1209 | Zbl

[137] Efimov N. V., “Vozniknovenie osobennostei na poverkhnostyakh otritsatelnoi krivizny”, Matem. sb., 64:2 (1964), 286–320 | Zbl

[138] Rozendorn E. R., Shikin E. V., “Raboty N. V. Efimova o poverkhnostyakh otritsatelnoi krivizny”, Matematika, K 100–letiyu so dnya rozhdeniya N. V. Efimova, v. VI, Sovremennye problemy matematiki i mekhaniki, 2, Izd–vo MGU, M., 2011, 49–56

[139] Vspominaem Nikolaya Vladimirovicha Efimova, MTsNMO, M., 2014

[140] Rozendorn E. R., “Postroenie ogranichennoi polnoi poverkhnosti nepolozhitelnoi krivizny”, UMN, 16:2 (1961), 149–156 | Zbl

[141] Rozendorn E. R., “Poverkhnosti otritsatelnoi krivizny”, Geometriya-3, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fund. naprav., 48, VINITI, M., 1989, 98–195

[142] Tikhonov A. N., Samarskii A. A. i dr., “Eduard Genrikhovich Poznyak (k semidesyatiletiyu so dnya rozhdeniya)”, UMN, 48:4 (1993), 245–247 | Zbl

[143] Poznyak E. G., “O regulyarnoi realizatsii v tselom dvumernykh rimanovykh metrik otritsatelnoi krivizny”, Matem. zametki, 1:2 (1967), 244–250 | Zbl

[144] Shikin E. V., “Izometricheskie pogruzheniya v $\mathbb{R}^3$ nekompaktnykh oblastei nepolozhitelnoi krivizny”, Itogi nauki i tekhn. Ser. Problemy geometrii. Tr. geom. sem., 7, VINITI, M., 1975, 249–265

[145] Poznyak E. G., “Ob izometricheskom pogruzhenii v trekhmernoe evklidovo prostranstvo dvumernykh mnogoobrazii otritsatelnoi krivizny”, Matem. zametki, 31:4 (1982), 601–612 | Zbl

[146] Tunitskii D. V., “O regulyarnom izometricheskom pogruzhenii v $E^3$ neogranichennykh oblastei otritsatelnoi krivizny”, Matem. sb., 133:1 (1987), 119–134 | Zbl

[147] Poznyak E. G., “Izometricheskie pogruzheniya dvumernykh rimanovykh metrik v evklidovy prostranstva”, UMN, 28:4 (1973), 47–76 | Zbl

[148] Poznyak E. G., Shikin E. V., “Poverkhnosti otritsatelnoi krivizny”, Itogi nauki i tekhn. Ser. Algebra. Topologiya. Geometriya, 12, VINITI, M., 1974, 171–207 | Zbl

[149] Poznyak E. G., Sokolov D. D., “Izometricheskie pogruzheniya rimanovykh prostranstv v evklidovy”, Itogi nauki i tekhn. Ser. Algebra. Topologiya. Geometriya, 15, VINITI, M., 1977, 173–211 | Zbl

[150] Poznyak E. G., Shikin E. V., “Malyi parametr v teorii izometricheskikh pogruzhenii dvumernykh rimanovykh mnogoobrazii v evklidovy prostranstva”, Itogi nauki i tekhn. Ser. Sovrem. matem. i ee pril. Tematicheskie obzory, 8, VINITI, M., 1995, 59–107

[151] Poznyak E. G., Popov A. G., “Geometriya uravneniya sin-Gordona”, Itogi nauki i tekhn. Ser. Problemy geometrii. Tr. geom. sem., 23, VINITI, M., 1991, 99–130

[152] Yanenko N. N., “Nekotorye voprosy teorii pogruzhenii rimanovykh metrik v evklidovy prostranstva”, UMN, 8:1 (1953), 21–100 | Zbl

[153] Yanenko N. N., “K teorii vlozheniya poverkhnostei v mnogomernom evklidovom prostranstve”, Tr. MMO, 3, 1954, 89–180 | Zbl

[154] Sabitov I. Kh., “Izometricheskie pogruzheniya i vlozheniya lokalno evklidovykh metrik v $R^2$”, Izv. RAN. Ser. Matem., 63:6 (1999), 147–166 | DOI | Zbl

[155] Sabitov I. Kh., “Izometricheskoe pogruzhenie lokalno evklidovykh metrik v $\mathbb{R}^3$”, Sib. matem. zhurn., 26:3 (1985), 156–167 | Zbl

[156] Mikhalev S. N., Sabitov I. Kh., “Izometricheskie vlozheniya lokalno evklidovykh metrik v $\mathbb{R}^3$ v vide konicheskikh poverkhnostei”, Matem. zametki, 95:2 (2014), 63–73 | DOI

[157] Mikhalev S. N., Sabitov I. Kh., “Izometricheskoe vlozhenie v $\mathbb{R}^3$ koltsa s lokalno evklidovoi metrikoi s tsilindricheskim tipom neodnoznachnosti”, Matem. zametki, 98:3 (2015), 378–385 | DOI | Zbl

[158] Sabitov I. Kh., “O razvertyvayuschikhsya lineichatykh poverkhnostyakh s maloi gladkostyu”, Sib. matem. zhurn., 50:5 (2009), 1163–1175 | Zbl

[159] Sabitov I. Kh., “O vneshnei krivizne i vneshnem stroenii $C^1$–gladkikh normalnykh razvertyvayuschikhsya poverkhnostei”, Matem. zametki, 87:6 (2010), 900–906 | DOI

[160] Sabitov I. Kh., Isometric immersions and embeddings of locally Euclidean metrics, v. 1, Rev. in Math. and Math. Phys., 13, Cambridge Scientific Publishers, Cambridge, 2008, 276 pp. | MR

[161] Shtogrin M. I., “Kusochno–gladkie razvertyvayuschiesya poverkhnosti”, Tr. MIAN, 263, 2008, 227–250 | Zbl

[162] Shtogrin M. I., “Izgibaniya razvertyvayuschiisya poverkhnosti s sokhraneniem ee rebra i obrazuyuschikh”, Tr. MIAN, 266, 2009, 263–271 | Zbl

[163] Shtogrin M. I., “Izometricheskie vlozheniya poverkhnostei platonovykh tel”, UMN, 62:2 (2007), 183–184 | DOI

[164] Shtogrin M. I., “O zamknutykh vypuklykh mnogogrannikakh, dopuskayuschikh nepreryvnye izgibaniya v klasse kusochno–gladkikh poverkhnostei”, Matematika, K 100–letiyu so dnya rozhdeniya N. V. Efimova, v. VI, Sovremennye problemy matematiki i mekhaniki, 3, Izd-vo MGU, M., 2011, 192–207 | Zbl

[165] Shtogrin M. I., “Izgibaniya kusochno–razvertyvayuscheisya poverkhnosti”, Tr. MIAN, 275, 2011, 144–166 | Zbl

[166] Dolbilin N. P., Shtanko M. A., Shtogrin M. I., “Neizgibaemost kvadrilyazha sfery”, Doklady RAN, 354:4 (1997), 443–445 | Zbl

[167] Dolbilin N. P., Shtanko M. A., Shtogrin M. I., “Neizgibaemost kvadrilyazha tora”, UMN, 54:4 (1999), 167–168 | DOI

[168] Shtogrin M. I., “Neizgibaemost kvadrilyazha krendelya”, UMN, 54:5 (1999), 183–184 | DOI

[169] Sabitov I. Kh., “Ob odnom klasse neizgibaemykh mnogogrannikov”, Sib. matem. zhurn., 55:5 (2014), 475–483

[170] Sabitov I. Kh., Ob'emy mnogogrannikov, 2–e izd., MTsNMO, M., 2009

[171] Alexandrov V., “An example of a flexible polyhedron with nonconstant volume in the spherical space”, Beiträge zur Algebra und Geometrie, 38:1 (1997), 11–18 | MR | Zbl

[172] Shtogrin M. I., “Ob izgibanii poliedralnoi poverkhnosti”, Tr. MIAN, 288, 2015, 171–183 | Zbl

[173] Bukhshtaber V. M., Erokhovets N. Yu., “Usecheniya prostykh mnogogrannikov i prilozheniya”, Tr. MIAN, 289, 2015, 115–144 | Zbl

[174] Sabitov I. Kh., “Ob'em mnogogrannika kak funktsiya ego metriki”, Fund. i prikl. matem., 2:4 (1996), 1235–1246 | Zbl

[175] Sabitov I. Kh., “Obobschennaya formula Gerona–Tartalya i nekotorye ee sledstviya”, Matem. sb., 189:10 (1998), 105–134 | DOI | Zbl

[176] Sabitov I. Kh., “Reshenie tsiklicheskikh mnogougolnikov”, Matematicheskoe prosveschenie. Tretya seriya, 11, MTsNMO, M., 2010, 83–106

[177] Gaifullin A. A., “Sabitov polynomials for volumes of polyhedra in four dimensions”, Adv. in Math., 252 (2014), 586–611 | DOI | MR | Zbl

[178] Gaifullin A. A., “Generalization of Sabitov's theorem to polyhedra of arbitrary dimensions”, Discrete and Comput. Geometry, 52:2 (2014), 195–220 | DOI | MR | Zbl

[179] Gaifullin A. A., “Analiticheskoe prodolzhenie ob'ema i gipoteza kuznechnykh mekhov v prostranstvakh Lobachevskogo”, Matem. sb., 206:11 (2015), 61–112 | DOI | Zbl

[180] Gaifullin A. A., “Vlozhennye izgibaemye sfericheskie kross–politopy s nepostoyannymi ob'emami”, Tr. MIAN, 288, 2015, 67–94 | Zbl

[181] Sabitov I. Kh., “Algoritmicheskoe reshenie problemy izometricheskoi realizatsii dvumernykh mnogogrannykh metrik”, Izv. RAN. Ser. Matem., 66:2 (2002), 159–172 | DOI | Zbl

[182] Sabitov I. Kh., “Algebraicheskaya teoriya reshenii mnogogrannikov”, UMN, 66:3 (2011), 3–66 | DOI