Geodesic
Almost product structures and Monge-Amp\`ere equations
Lobachevskii journal of mathematics, Tome 23 (2006), pp. 151-181.

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Tensor invariants of an almost product structure are constructed. We apply them to solving the problem of contact equivalence and the problem of contact linearization for Monge-Ampère equations. 
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A. G. Kushner. Almost product structures and Monge-Amp\`ere equations. Lobachevskii journal of mathematics, Tome 23 (2006), pp. 151-181. http://geodesic.mathdoc.fr/item/LJM_2006_23_a5/

[1] Hunter J. K., Saxton R., “Dynamics of Director Fields”, SIAM J. Appl. Math., 51:6 (1991), 1498–1521 | DOI | MR | Zbl

[2] Kiritchenco V., Differential-geometrical Structures on Manifolds, Moscow State Pedagogical University, Moscow, 2003, 496 pp.

[3] Kruglikov B. S., “On Some Classification Problems in Four-Dimensional Geometry: Distributions, Almost Complex Structures, and the Generalized Monge-Ampère Equations”, Mat. Sb., 189:11 (1998), 61–74 | MR | Zbl

[4] Kruglikov B. S., “Symplectic and Contact Lie Algebras with Application to the Monge-Ampère Equations”, Tr. Mat. Inst. Steklova, 221, 1998, 232–246 | MR | Zbl

[5] Kruglikov B. S., “Classification of Monge-Ampère Equations With Two Variables”, CAUSTICS '98 (Warsaw), Polish Acad. Sci., Warsaw, 1999, 179–194 | MR | Zbl

[6] Kushner A., “Classification of Mixed Type Monge-Ampère Equations”, Geometry in Partial Differential Equations, World Sci. Publ., River Edge, NJ, 1993, 173–188 | MR

[7] Kushner A., “Symplectic Geometry of Mixed Type Equations”, Amer. Math. Soc. Transl. Ser. 2, 1995, 131–142 | MR | Zbl

[8] Kushner A., “Monge-Ampère Equations and e-Structures”, Dokl. Akad. Nauk, 361:5 (1998), 595–596 | MR | Zbl

[9] Kushner A., “Contact Linearization of Nondegenerate Monge-Ampère Equations”, Dvigenia v obobshennyh prostranstvah, PGPU, Penza, 2005, 56–65 (in Russian)

[10] Kushner A., Lychagin V., Rubtsov V., Contact Geometry and Nonlinear Differential Equations, Cambridge University Press, 2006 (to appear)

[11] Lychagin V. V., “Contact Geometry and Second-Order Nonlinear Differential Equations”, Uspekhi Mat. Nauk, 34:1 (1979), 137–165 | MR | Zbl

[12] Lychagin V., Lectures on Geometry of Differential Equations, 1, 2, La Sapienza, Rome, 1993

[13] Lychagin V. V. and Rubtsov V. N., “Non-holonomic Filtration: Algebraic and Geometric Aspects of Non-Integrability”, Geometry in partial differential equations, World Sci. Publishing, River Edge, NJ, 1994, 189–214 | MR | Zbl

[14] Morozov O. I., Contact Equivalence of the Generalized Hunter-Saxton Equation and the Euler-Poisson Equation, arXiv:math-ph/0406016

[15] Tunitskii D. V., “On the Contact Linearization of Monge-Ampère Equations”, Izv. Ross. Akad. Nauk Ser. Mat., 60:2 (1996), 195–220 | MR

[16] Yano K., “On a structure defined by a tensor field of type $(1,1)$ satisfying $f^{3}+f=0$”, Tensor N.S., 14 (1963), 99–109 | MR | Zbl