APPLICATION OF CARTAN’S EQUIVALENCE METHOD TO DISTRIBUTION OF PLANES
Abstract
In this paper, we apply Cartan’s equivalence method to distribution of planes to give a proof of the local equivalence between two planes.
References
[1]A. G. Kushner, Classification of mixed type Monge-Ampère equations, Geometry in Partial Differential Equations, World Sci. Publ., River Edge, NJ, 1994, pp. 173-188.
[2]A. G. Kushner, A contact linearization problem for Monge-Ampère equations and Laplace invariants, Acta Appl. Math. 101(1) (2008), 177-189.
[3]A. G. Kushner, On contact equivalence of Monge-Ampère equations to linear equations with constant coefficients, Acta Appl. Math. 109(1) (2010), 197-210.
[4]B. S. Kruglikov, Classification of Monge-Ampère equations with two variables, Geometry and topology of caustics — CAUSTICS ‘98 (Warsaw), Banach Center Publ., 50, Polish Acad. Sci. Inst. Math., Warsaw, 1999, pp. 179-194.
[5]I. Moheddine, Géométrie de Cartan fondée sur la notion d’aire et application du problème d’équivalence, Ph.D. Thesis, 2012.
[6]I. Moheddine, Application of equivalence method to classify Monge-Ampère equations of elliptic type, The Australian Journal of Mathematical Analysis and Applications (AJMAA) 11(1) (2014), 1-13, Article 12.
[7]V. Lychagin and V. Rubtsov, Local classification of Monge-Ampère equations, Soviet Math. Dokl. 28(2) (1983), 328-332.
[8]N. Sylvain, Implantation et nouvelles applications de la méthode d’équivalence de Cartan, Ph.D. Thesis, 2003.
[9]P. J. Olver, Equivalence, Invariants, and Symmetry, Cambridge University Press, Cambridge, 1995.
[10]Robert Bryant, Phillip Griffiths and Daniel Grossman, Exterior differential systems and Euler-Lagrange partial differential equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2003.
[11]T. Morimoto, La géométrie des équations de Monge-Ampère, C. R. Acad. Sci. Paris Sér. A-B 289(1) (1979), A25-A28.
[12]T. Morimoto, Le problème d’équivalence des équations de Monge-Ampère, C. R. Acad. Sci. Paris Sér I. Math. 289 (1979), 63-66.
[13]V. Lychagin, A. Kushner and V. Rubtsov, Contact geometry and non-linear differential equations, Encyclopedia of Mathematics and its Application, Volume 61, Cambridge University Press, Cambridge, 2007.
[14]V. Lychagin, Lectures on Geometry of Differential Equations, Volume 1, La Sapienza, Rome, 1993.
[15]V. Lychagin, V. N. Rubtsov and I. V. Chekalov, A classification of Monge-Ampère equations, Ann. Sci. École Norm. Sup. (4) 26(3) (1993), 281-308.
[16]