On Ricci-quadratic Finsler metrics

Abstract

In this paper, the Ricci curvature is defined for sprays on a manifold and every spray with a volume form on a manifold can be deformed to a projective spray. The quadratic Ricci curvature of a projective spray is called the quadratic projective Ricci curvature. We study and characterize quadratic (projective) Ricci curvature for Finsler metrics, in particular for Randers metrics