Ricci-quadratic homogeneous Randers spaces

Abstract

A Finsler space is called Ricci-quadratic if its Ricci curvature Ric(x,y) is quadratic in y. It is called a Berwald space if its Chern connection defines a linear connection directly on the underlying manifold M. In this article, we prove that a homogeneous Randers space is Ricci-quadratic if and only if it is of Berwald type.