DIPS 1/2008 [tex source, PostScript, PDF file, dvi]

Title: On geometry of second order parabolic differential equations in two independent variables.

Author: A. M. Vinogradov

In this note we announce some new results concerning second order differential parabolic equation in two independent variables. It turns out that any such equation is of Monge-Ampere type. These latter are characterized by the fact that the associated subsidiary equations describing singularities of their multivalued solutions has, in a sense, the simplest form. The structure of these subsidiary equations allows to subdivide parabolic equations into four classes. Each of them can be described as a special geometrical structure on 4-dimensional manifolds introduced below. Beside other, this leads to a complete classification of considered parabolic equations with respect to the group of contact transformation.
Our approach differs from the traditional one by the fact that we focus on the corresponding subsidiary, or characteristic, equations rather than on original ones. This leads to a noteworthy simplification.

Last revised November 25, 2008. 6 pages, LaTeX-2e.

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