Pseudo-Riemannian and Hessian Geometry Related to Monge-Ampère Structures

Abstract

We study properties of pseudo-Riemannian metrics corresponding to Monge-Ampère structures on four-dimensional $T^{\ast }M$. We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Plücker embedding equation. We also focus on pullbacks of the pseudo-metrics on two-dimensional $M$ and describe the corresponding Hessian structures.