26 Feb 2003

Alexei Kushner (Astrakhan University, Russia) "Geometry of mixed type equations".

In this lecture we consider the equivalence problem for mixed type Monge-Ampere equations. We will show that such equations in a general position can be considered as an {e}-structure (absolute parallelism) on the cotangent bundle. We will also consider two classical linear mixed type equations: Chaplygin's and Keldysh's, describe their geometry and solve the problem of equivalence (normal forms) of a Monge-Ampere equation to one of these equations.