A Contact Linearization Problem for Monge-Ampère Equations and Laplace Invariants

Abstract

We solve a problem of contact linearization for non-degenerate regular MongeAmpère equations. In order to solve the problem we construct tensor invariants of equations with respect to contact transformations and generalize the classical Laplace invariants.

On Contact Equivalence of Monge-Ampère Equations to Linear Equations with Constant Coefficients

“…where j, k, s = 1, 2, 3; s = j, k. Here P j : D(J 1 M) → D j is the projector from the module of vector fields D(J 1 M) on J 1 M to the module of vector fields D j on the distribution P j (j = 1, 2, 3) (see [15]). …”

“…Due to the theorem of contact linearization [15], the equation E is locally contact equivalent to linear equation of the form:…”

“…Since the Laplace forms for elliptic equations are complex conjugate [15], all elliptic Monge-Ampère equations split into two classes: H 1,1 and H 2,2 .…”

“…The present paper can be considered as continuation of the paper [15]. Here we give a complete solution of the following problem for hyperbolic and elliptic Monge-Ampère equations:…”

“…A contact linearization problem for general hyperbolic and elliptic Monge-Ampère equations was solved by author in the series of papers [14][15][16].…”