A classification of Monge-Ampère equations
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 26 (1993) no. 3, pp. 281-308.
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     author = {Lychagin, V. V. and Rubtsov, V. N. and Chekalov, I. V.},
     title = {A classification of {Monge-Amp\`ere} equations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {281--308},
     publisher = {Elsevier},
     volume = {Ser. 4, 26},
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     doi = {10.24033/asens.1673},
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     zbl = {0789.58078},
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     url = {http://archive.numdam.org/articles/10.24033/asens.1673/}
}
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Lychagin, V. V.; Rubtsov, V. N.; Chekalov, I. V. A classification of Monge-Ampère equations. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 26 (1993) no. 3, pp. 281-308. doi : 10.24033/asens.1673. http://archive.numdam.org/articles/10.24033/asens.1673/

[1] E. Andreey, E. Vinberg and A. Elashvili, Orbits of the Highest Dimension of Semisimple Linear Lie Groups (Funct. Analiz i ego prilozeniya, Vol. 1, 1967, No. 4, pp. 3-7, Russian) ; English transl. in Funct. Anal. Appl. 1, 1968. | Zbl

[2] E. Artin, Geometric Algebra, Academic Press, New York, 1959.

[3] N. Bourbaki, Groupes et algèbres de Lie, ch. VI et VII, Hermann, Paris, 1975.

[4] E. Cartan, Oeuvre Complète, Dunod, Paris.

[5] I. Chekalov and V. Rubtsov, Stabilizors of Some Reductive Lie Subalgebras and Monge-Ampère Equations (Russian), Proceedings of the 17-th All-Union, Algebraic Conference, Part II, 1983, Minsk, pp. 201-202.

[6] Goldschmidt H., Integrability Criteria for Systems of Nonlinear Partial Differential Equations (J. Differential Geometry, Vol. 1, 1967, pp. 269-307). | MR | Zbl

[7] V. Guillemin and S. Sternberg, An Algebraic Model of Transitive Differential Geometry (Bull. Amer. Math. Soc., Vol. 70, 1964, pp. 16-47). | MR | Zbl

[8] J.-I. Igusa, A Classification of Spinors up to Dimension Twelve (Amer. Math. Journ., Vol. 92, 1972, pp. 997-1028). | MR | Zbl

[9] S. Kobayashi and T. Nagano, On Filtered Lie Algebras and Geometric Structures, III (J. Math. Mech., Vol. 14, 1965, pp. 679-706). | MR | Zbl

[10] I. Krasilschik, V. Lychagin and A. Vinogradov, Geometry of Jet Spaces and Non-Linear Partial Differential Equations, Gordon & Breach, London, 1986. | Zbl

[11] S. Lie, Gessamelte Abhandlungen, Band VI, Aschehoug, Oslo and Teubner, Leipzig, 1922.

[12] V. Lychagin, Local Classification of Non-Linear First-Order Partial Differential Equations (Russian Math. Surveys, Vol. 30, 1975, pp. 105-176). | Zbl

[13] V. Lychagin, On Sufficient Orbits of Contact Diffeomorphisms Group (Mat. Sb., Vol. 104, 146, 1977, pp. 248-270, Russian) ; English transl. in Nath. USSR Sb., Vol. 33, 1977. | Zbl

[14] V. Lychagin, Non-Linear Differential Equations and Contact Geometry (Uspekhi Mat. Nauk., Vol. 34, 1 (205), 1979, pp. 137-165, Russian) ; English transl. in Russian Math. Surveys, Vol. 34, 1979.

[15] V. Lychagin and V. Rubtsov, On Sophus Lie Theorems for Monge-Ampère Equations (Russian), Doklady Bielorrusian Academy of Science, Vol. 27, 5, 1983, pp. 396-398. | MR | Zbl

[16] V. Lychagin and V. Rubtsov, Local Classification of Monge-Ampère Equations (Soviet Math. Dokl., Vol. 28, 2, 1983, pp. 328-332). | MR | Zbl

[17] T. Morimoto, Le problème d'équivalence des équations de Monge-Ampère (C.R. Acad. Sci., Paris, Ser I, Math., Vol. 289, 1979, pp. 63-66). | MR

[18] A. Onischik, Splitting of Reductive Lie Groupes (Mat. Sb., Vol. 80, 122, 1969, pp. 553-599, Russian) ; English transl. in Math. USSR Sb. 25, 1969.

[19] V. Popov, Classification of Spinors of Dimension 14, Trudy MMO, Vol. 37, 1978, pp. 173-217 (Russian). | MR | Zbl

[20] J.-P. Serre, Faisceaux algébriques cohérents (Ann. Math., Vol. 61, 1955, pp. 197-278). | MR | Zbl

[21] I. Singer and S. Sternberg, On the Infinite Groups of Lie and Cartan (J. d'Analyse Mathématique, Vol. 15, 1965, pp. 1-114). | MR | Zbl

[22] D. C. Spencer, Overdetermined Systems of Linear Partial Differential Equations (Bull. Amer. Math. Soc., Vol. 75, 1969, pp. 179-239). | MR | Zbl

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