Geodesic
Equivalence and characteristic connections of the Monge–Ampere equations
Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 771-797 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The present paper is devoted to the problem of contact equivalence of the Monge–Ampere equations with two independent variables. When the Monge–Ampere equation is in general position an affine connection can be associated with it in a natural manner. This association enables us to formulate and prove a number of criteria for the contact equivalence of the Monge–Ampere equations in general position that make use of the corresponding properties of affine connections. 
@article{SM_1997_188_5_a6,
     author = {D. V. Tunitsky},
     title = {Equivalence and characteristic connections of {the~Monge{\textendash}Ampere} equations},
     journal = {Sbornik. Mathematics},
     pages = {771--797},
     year = {1997},
     volume = {188},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_5_a6/}
}
TY  - JOUR
AU  - D. V. Tunitsky
TI  - Equivalence and characteristic connections of the Monge–Ampere equations
JO  - Sbornik. Mathematics
PY  - 1997
SP  - 771
EP  - 797
VL  - 188
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_1997_188_5_a6/
LA  - en
ID  - SM_1997_188_5_a6
ER  - 
%0 Journal Article
%A D. V. Tunitsky
%T Equivalence and characteristic connections of the Monge–Ampere equations
%J Sbornik. Mathematics
%D 1997
%P 771-797
%V 188
%N 5
%U http://geodesic.mathdoc.fr/item/SM_1997_188_5_a6/
%G en
%F SM_1997_188_5_a6
D. V. Tunitsky. Equivalence and characteristic connections of the Monge–Ampere equations. Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 771-797. http://geodesic.mathdoc.fr/item/SM_1997_188_5_a6/

[1] Lychagin V. V., “Kontaktnaya geometriya i nelineinye differentsialnye uravneniya vtorogo poryadka”, UMN, 34:1(205) (1979), 137–165 | MR | Zbl

[2] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[3] Kobayasi Sh., Gruppy preobrazovanii v differentsialnoi geometrii, Mir, M., 1986 | MR

[4] Lie S., “Kurzes Résumé mehrerer neuer Theorien”, Gesammelte Abhandlungen, Bd. 3, B. G. Teubner, Oslo; H. Aschehoug Co, Leipzig, 1922, 1–4

[5] Lie S., “Neue Integrationsmethode der Monge–Ampèreschen Gleichung”, Gesammelte Abhandlungen, Bd. 3, B. G. Teubner, Oslo; H. Aschehoug Co, Leipzig, 1922, 287–294

[6] Lie S., “Untersuchungen üb Differentialgleihungen”, Gesammelte Abhandlungen, Bd. 3, B. G. Teubner, Oslo; H. Aschehoug Co, Leipzig, 1922, 537–547

[7] Goursat E., Lecons sur l'intégration des équations aux dérivées partielles du second ordre, V. 1, Hermann, Paris, 1896 | Zbl

[8] Lychagin V. V., Rubtsov V. N., “O teoremakh Sofusa Li dlya uravnenii Monzha–Ampera”, DAN BSSR, 27:5 (1983), 396–398 | MR | Zbl

[9] Lychagin V. V., Rubtsov V. N., Chekalov I. V., “A classification of Monge–Ampère equations”, Ann. scient. Éc. Norm. Sup. 4 série, 26 (1993), 281–308 | MR | Zbl

[10] Morimoto T., “La géométrie des équations Monge–Ampère”, C. R. Acad. Sc. Paris. Série A, 289 (1979), 25–28 | MR | Zbl

[11] Postnikov M. M., Differentsialnaya geometriya, Nauka, M., 1988 | MR | Zbl

[12] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, T. 1, Nauka, M., 1981

[13] Volf Dzh., Prostranstva postoyannoi krivizny, Nauka, M., 1982 | MR