Contact geometry of hyperbolic Monge–Ampère equations

This paper is devoted to the geometry of hyperbolic Monge–Ampère equations with large symmetry algebras. We classify all hyperbolic Monge–Ampère equations whose Lie algebra of contact symmetries is transitive. We also give the explicit construction for Cartan connections associated with generic hyperbolic Monge–Ampère equations and find those equations which correspond to connections with vanishing curvature tensor.