Long-time existence of a geometric flow on closed Hessian manifolds

Abstract

In this paper we study Hessian manifolds. We define a flow, which we call the Hessian flow, to study the existence of Einstein–Hessian metrics on Hessian manifolds. The flow will considered as a real Monge–Ampére equation and we prove the short-time existence, the global existence and the uniqueness of it.