Geodesic
Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge–Ampere equations
Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1643-1656 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Three related classification problems on four-manifolds are discussed. First, regular distributions are considered and described locally. After that a classification of almost complex structures of general position in terms of distributions is proposed. Finally, non-degenerate generalized Monge–Ampere equations are classified in terms of $\{e\}$-structures. Symplectic Lie algebras are also considered in an appendix. 
@article{SM_1998_189_11_a2,
     author = {B. S. Kruglikov},
     title = {Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized {Monge{\textendash}Ampere} equations},
     journal = {Sbornik. Mathematics},
     pages = {1643--1656},
     year = {1998},
     volume = {189},
     number = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_11_a2/}
}
TY  - JOUR
AU  - B. S. Kruglikov
TI  - Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge–Ampere equations
JO  - Sbornik. Mathematics
PY  - 1998
SP  - 1643
EP  - 1656
VL  - 189
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/SM_1998_189_11_a2/
LA  - en
ID  - SM_1998_189_11_a2
ER  - 
%0 Journal Article
%A B. S. Kruglikov
%T Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge–Ampere equations
%J Sbornik. Mathematics
%D 1998
%P 1643-1656
%V 189
%N 11
%U http://geodesic.mathdoc.fr/item/SM_1998_189_11_a2/
%G en
%F SM_1998_189_11_a2
B. S. Kruglikov. Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge–Ampere equations. Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1643-1656. http://geodesic.mathdoc.fr/item/SM_1998_189_11_a2/

[1] Sternberg S., Lektsii po differentsialnoi geometrii, Mir, M., 1970 | MR | Zbl

[2] Alekseevskii D. V., Vinogradov A. M., Lychagin V. V., “Osnovnye idei i ponyatiya differentsialnoi geometrii”, Geometriya–1, Itogi nauki i tekhn. Sovr. probl. matem. Fundam. napr., 28, VINITI, M., 1988, 5–297

[3] Kruglikov B. S., Some classificational problems in four dimensional geometry: distributions, almost complex structures and Monge–Ampere equations, Preprint of the University of Tromsoe, No 96-17

[4] Kruglikov B. S., “Tenzory Nienkheisa i prepyatstviya k postroeniyu psevdogolomorfnykh otobrazhenii”, Matem. zametki, 63:4 (1998), 541–561 | MR | Zbl

[5] Bouzon J., “Structures presque-cocomplexes”, Univ. et Polytech. Torino Rend. Sem. Nat., 24 (1964/1965), 53–123 | MR

[6] Sasaki S., “On differentiable manifolds with certain structures which are closely related to almost contact structures”, Tôhoku Math. J., 12 (1960), 459–476 ; “On differentiable manifolds with certain structures which are closely related to almost contact structures, II”, Tôhoku Math. J., 13 (1961), 281–294 (with Y. Hatakeyama) | DOI | MR | Zbl | DOI | MR | Zbl

[7] Lychagin V., “Lectures on geometry of differential equations”, Ciclo di conferenze tenute presso il Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate Università “La Sapienza” (Roma, 1992)

[8] Kushner A., “Symplectic geometry of mixed type equations”, Amer. Math. Soc. Transl., 167 (1995), 131–142 | MR | Zbl

[9] Lychagin V. V., “Kontaktnaya geometriya i nelineinye differentsialnye uravneniya vtorogo poryadka”, UMN, 34:1 (1979), 137–165 | MR | Zbl

[10] Cartan E., “Les systèmes de Pfaff à cinq variables et les équations aux derivées partielles du second ordre”, Ann. Ec. Normale, 27 (1910), 109–192 ; Euvres Completes, Gautier-Villars, Paris, 1953 | MR | Zbl

[11] Tanaka N., “On differential systems, graded Lie algebras and pseudogroups”, J. Math. Kyoto Univ., 10 (1970), 1–82 | MR | Zbl

[12] Newlander A., Nirenberg L., “Complex analytic coordinates in almost-complex manifolds”, Ann. of Math. (2), 65:3 (1957), 391–404 | DOI | MR | Zbl

[13] Lychagin V. V., Rubtsov V. N., Chekalov I. V., “A classification of Monge–Ampère equations”, Ann. Sci. Ecole Norm. Sup. (4), 26:3 (1992), 281–308 | MR

[14] Libermann P., Marle C.-M., Symplectic geometry and analytical mechanics, D. Reidel Publishing Company, Dordrecht, 1987 | MR | Zbl

[15] Frölicher A., Nijenhuis A., “Theory of vector-valued differential forms, II”, Proc. Konink. Nederl. Akad. Wetensch., 59:3 (1956), 338–359 | Zbl

[16] Seminar “Sofus Li”. Teoriya algebr Li. Topologiya grupp Li, Biblioteka sbornika “Matematika”, IL, M., 1962

[17] Dzhekobson N., Algebry Li, Mir, M., 1964 | MR

[18] Kruglikov B. S., “Simplekticheskie i kontaktnye algebry Li s prilozheniem k uravneniyu Monzha–Ampera”, Tr. MIAN, 221, Nauka, M., 1998, 232–246 (to appear) | MR | Zbl