CONTACT EQUIVALENCE OF MONGE-AMP\`ERE EQUATIONS
WITH TRANSITIVE SYMMETRIES

Dimitry V. Tunitsky

Key words: Monge-Amp\`ere equation, characteristic bundle,
        contact equivalence, characteristic affine connection,
        invariance with respect to parallelism, contact symmetry,
        homogeneous M-A equation.

1991 Math. Subject Classification: 58G03, 58G16, 53C07, 53C30.

Abstract: This paper deals with Monge-Amp\`ere equations on
5-dimensional contact manifolds, i.e., M-A equations with two
independent variables. If a M-A equation is in general position,
then the unique affine connection can be put into correspondence
with this equation in natural manner. This correspondence allows
to formulate and prove a number of results on contact
equivalence of M-A equations with transitive symmetry group
using suitable properties of affine connections.