Bending of a~piecewise developable surface
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 144-166.

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

We substantiate in detail the possibility of one-parameter bending of a developable surface possessing a stationary curvilinear edge and stationary rectilinear generators. We construct particular examples of developable surfaces that possess a curvilinear edge and admit one-parameter bendings. We also give examples of closed piecewise developable surfaces that admit one-parameter bendings.
@article{TM_2011_275_a7,
     author = {M. I. Shtogrin},
     title = {Bending of a~piecewise developable surface},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {144--166},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_275_a7/}
}
TY  - JOUR
AU  - M. I. Shtogrin
TI  - Bending of a~piecewise developable surface
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2011
SP  - 144
EP  - 166
VL  - 275
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2011_275_a7/
LA  - ru
ID  - TM_2011_275_a7
ER  - 
%0 Journal Article
%A M. I. Shtogrin
%T Bending of a~piecewise developable surface
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2011
%P 144-166
%V 275
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2011_275_a7/
%G ru
%F TM_2011_275_a7
M. I. Shtogrin. Bending of a~piecewise developable surface. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 144-166. http://geodesic.mathdoc.fr/item/TM_2011_275_a7/

[1] Shtogrin M.I., “Izgibanie razvertyvayuscheisya poverkhnosti s sokhraneniem ee rebra i obrazuyuschikh”, Tr. MIAN, 266, 2009, 263–271 | MR | Zbl

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

[3] Pogorelov A.V., Geometricheskie metody v nelineinoi teorii uprugikh obolochek, Nauka, M., 1967 | MR

[4] Shtogrin M.I., “Spetsialnye izometricheskie preobrazovaniya tsilindra”, UMN, 62:5 (2007), 173–174 | DOI | MR | Zbl

[5] Shtogrin M.I., “Spetsialnye izometricheskie preobrazovaniya konusa”, UMN, 63:2 (2008), 183–184 | DOI | MR | Zbl

[6] Shtogrin M.I., “Izometricheskie pogruzheniya konusa i tsilindra”, Izv. RAN. Ser. mat., 73:1 (2009), 187–224 | DOI | MR | Zbl

[7] Mischenko A.S., Solovev Yu.P., Fomenko A.T., Sbornik zadach po differentsialnoi geometrii i topologii, Fizmatlit, M., 2001

[8] Aleksandrov V.A., “Novyi primer izgibaemogo mnogogrannika”, Sib. mat. zhurn., 36:6 (1995), 1215–1224 | MR | Zbl

[9] Konnelli R., “Ob odnom podkhode k probleme neizgibaemosti”, Issledovaniya po metricheskoi teorii poverkhnostei, Matematika. Novoe v zarubezhnoi nauke, 18, Mir, M., 1980, 164–209 | MR

[10] R. Connelly, “The rigidity of certain cabled frameworks and the second-order rigidity of arbitrarily triangulated convex surfaces”, Adv. Math., 37:3 (1980), 272–299 | DOI | MR | Zbl

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

[12] Zalgaller V.A., “Nekotorye izgibaniya dlinnogo tsilindra”, Zap. nauch. sem. POMI, 246 (1997), 66–83 | MR | Zbl

[13] Shtogrin M.I., “Polozhitelnost krivizny i vypuklost granei”, Tr. MIAN, 252, 2006, 277–284 | MR

[14] Sabitov I.Kh., “Obobschenie teoremy Pogorelova–Stokera o polnykh razvertyvayuschikhsya poverkhnostyakh”, Fund. i prikl. matematika, 12:1 (2006), 247–252 | MR

[15] Sabitov I.Kh., “Ob'em mnogogrannika kak funktsiya dlin ego reber”, Fund. i prikl. matematika, 2:1 (1996), 305–307 | MR | Zbl

[16] Slovesnov A.V., “Lenty Mebiusa s ploskoi metrikoi”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 2009, no. 5, 7–10 | MR

[17] Shtogrin M.I., “Spetsialnye vlozheniya krugovogo konusa”, Geometriya “v tselom”, topologiya i ikh prilozheniya, Tr. Mezhdunar. konf., posv. 90-letiyu A.V. Pogorelova, Akta, Kharkov, 2010, 96–113

[18] Sabitov I.Kh., Isometric immersions and embeddings of locally Euclidean metrics, Rev. Math. and Math. Phys., 13, no. 1, Cambridge Sci. Publ., Cambridge, 2008 | MR | Zbl