Geodesic
Equivalence and characteristic connections of the Monge–Ampere equations
Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 771-797 
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/
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     title = {Equivalence and characteristic connections of {the~Monge{\textendash}Ampere} equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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