Ricci-quadratic homogeneous Randers spaces

TL;DR

This paper proves that homogeneous Randers spaces are Ricci-quadratic if and only if they are of Berwald type, establishing a precise equivalence between these geometric properties.

Contribution

It provides a complete characterization of Ricci-quadratic homogeneous Randers spaces as exactly those of Berwald type.

Findings

Homogeneous Randers spaces are Ricci-quadratic iff they are Berwald spaces.

Established the equivalence between Ricci-quadratic and Berwald properties in this context.

Clarified the geometric structure of 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.