@article{bwmeta1.element.bwnjournal-article-bcpv39z1p105bwm,
author = {Morimoto, Tohru},
title = {Monge-Amp\`ere equationsviewed from contact geometry},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {105-121},
zbl = {0879.35008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p105bwm}
}
Morimoto, Tohru. Monge-Ampère equationsviewed from contact geometry. Banach Center Publications, Tome 38 (1997) pp. 105-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p105bwm/
[000] R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior differential systems, Springer-Verlag New York, 1991. | Zbl 0726.58002
[001] R. L. Bryant and P. A. Griffiths, Characteristic cohomology of differential systems I: General theory, J. Amer. Math. Soc. 8 (1995), 507-627. | Zbl 0845.58004
[002] R. L. Bryant and P. A. Griffiths, Characteristic cohomology of differential systems II: Conservation laws for a class of parabolic equations, Duke Math. J. 78 (1995), 531-676. | Zbl 0853.58005
[003] É. Cartan, Les systèmes de Pfaff à cinq variables et les équations aux dérivées partielles du second ordre, Ann. École Norm. Sup. 27 (1910), 109-192. | Zbl 41.0417.01
[004] É. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, Paris, 1945. | Zbl 0211.12701
[005] B. Doubrov and A. Kushner, The Morimoto equation, ISLC Mathematical College Works, Lie-Lobachevsky Colloquium, Tartu, October 26-30, 1992, International Sophus Lie Centre, 1992, 30-32.
[006] A. F. Forsyth, Theory of differential equations, IV, Cambridge Univ. Press, London, 1906.
[007] R. B. Gardner, Invariants of Pfaffian systems, Trans. Amer. Math. Soc. 126 (1967), 514-533. | Zbl 0161.41301
[008] R. B. Gardner, The Cauchy problem for Pfaffian systems, Comm. Pure Appl. Math. 22 (1969), 587-596. | Zbl 0182.42601
[009] R. B. Gardner, A differential geometric generalization of characteristics, Comm. Pure Appl. Math. 22 (1969), 597-626. | Zbl 0182.42602
[010] R. B. Gardner, Characteristics and the geometry of hyperbolic equations in the plane, J. Differential Equations 104 (1993), 60-116. | Zbl 0797.35122
[011] E. Goursat, Leçon sur l'intégration des équations aux derivées partielles du second ordre à deux variables independentes, I, II, Hermann, Paris, 1896, 1898.
[012] D. Hartley, R. W. Tucker, and P. A. Tuckey, Equivalence of the Darboux and Gardner methods for integrating hyperbolic equations in the plane, Duke Math. J. 77 (1995), 167-192. | Zbl 0823.35121
[013] G. Ishikawa, Determinacy of the envelope of the osculating hyperplanes to a curve, Bull. London Math. Soc. 25 (1993), 603-610. | Zbl 0801.58006
[014] G. Ishikawa, Developable of a curve and determinacy relative to osculation-type, Quart. J. Math. Oxford Ser. (2) 46 (1995), 437-451. | Zbl 0854.53001
[015] G. Ishikawa and T. Morimoto, On solution surfaces of Monge-Ampère equations, in preparation. | Zbl 0991.58009
[016] M. Kossowski, Homotopy invariants for solutions to symplectic Monge-Ampère equations, J. Differential Equations 106 (1993), 294-311. | Zbl 0797.58024
[017] M. Kuranishi, Lectures on exterior differential systems, Tata Institute of Fundamental Research, Bombay, 1962. | Zbl 0106.15303
[018] Th. Lepage, Sur certaine formes différentielles associées aux équations du type de Monge-Ampère provenant du calcul des variations, Bulletins de la Classe des Sciences, Académie Royale de Belgique, 15 (1929), 829-848. | Zbl 55.0899.03
[019] Th. Lepage, Sur une propriété caractéristique des équations des extrémales des intégrales multiples, Bulletins de la Classe des Sciences, Académie Royale de Belgique, 16 (1930), 103-123. | Zbl 56.1082.03
[020] Th. Lepage, Interprétation géométrique de certains résultats de la théorie des formes symboliques de différentielles. Première communication, Bulletins de la Classe des Sciences, Académie Royale de Belgique, 16 (1930), 1334-1352. | Zbl 56.1029.01
[021] Th. Lepage, Interprétation géométrique de certains résultats de la théorie des formes symboliques de différentielles. Deuxième communication, Bulletins de la Classe des Sciences, Académie Royale de Belgique, 17 (1931), 163-178. | Zbl 57.0497.03
[022] Th. Lepage, Sur certaines formes différentielles symboliques de degré et de rang n à 2n + 1 variables, Bulletins de la Classe des Sciences, Académie Royale de Belgique, 20 (1934), 527-537. | Zbl 0009.35402
[023] V. V. Lychagin, Contact geometry and non-linear second order differential equations, Russian Math. Surveys 34 (1979), 149-180. | Zbl 0427.58002
[024] V. V. Lychagin, V. N. Rubtsov and I. V. Chekalov, A classification of Monge-Ampère equations, Ann. Sc. École Norm. Sup. (4) 26 (1993), 281-308. | Zbl 0789.58078
[025] M. Matsuda, Two methods of integrating Monge-Ampère equations, Trans. Amer. Math. Soc. 150 (1970), 327-343. | Zbl 0201.42101
[026] M. Matsuda, Two methods of integrating Monge-Ampère equations, II, Trans. Amer. Math. Soc. 166 (1972), 371-386. | Zbl 0235.35002
[027] M. Matsuda, On Monge-Ampère equations, Sugaku 24-2 (1972), 100-118 (in Japanese).
[028] M. Matsuda, Reduction of Monge-Ampère's equations by Imschenetsky transformations, J. Math. Soc. Japan 25 (1973), 43-70. | Zbl 0243.35066
[029] M. Matsuda, Theory of exterior differential forms, Iwanamishoten, Tokyo, 1976 (in Japanese).
[030] T. Morimoto, La géométrie des équations de Monge-Ampère, C. R. Acad. Sci. Paris 289 (1979), A-25-A-28. | Zbl 0425.35023
[031] T. Morimoto, Open problems suggested by T. Morimoto, Open problems in structure theory of non-linear integrable differential and difference systems: Proceedings of the fifteenth international symposium, Division of Mathematics, The Taniguchi Foundation, 1984, 27-29.
[032] T. Morimoto, On Monge-Ampère equations, Sûrikaisekikenkyûsho Kôkyûroku (Real Singularities and Real Algebraic Geometry) 815 (1992), 97-109 (in Japanese).
[033] T. Morimoto, Geometric structures on filtered manifolds, Hokkaido Math. J. 22 (1993), 263-347. | Zbl 0801.53019
[034] I. M. Singer and S. Sternberg, On the infinite groups of Lie and Cartan, Part I (The transitive groups), J. Anal. Math. 15 (1965), 1-114. | Zbl 0277.58008
[035] N. Tanaka, On differential systems, graded Lie algebras and pseudo-groups, J. Math. Kyoto Univ. 10 (1970), 1-82. | Zbl 0206.50503
[036] M. Tsuji, Formation of singularities for Monge-Ampère equations, Bull. Soc. Math. France 119 (1995), 433-457. | Zbl 0845.35005
[037] D. V. Tunitsky, Hyperbolicity and multivalued solutions of Monge-Ampère equations, Amer. Math. Soc. Transl. Ser. 2 167 (1995), 245-260. | Zbl 0836.35097