On the flag curvature of invariant Randers metrics

TL;DR

This paper derives explicit formulas for the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups, investigates conditions for constant positive flag curvature, and explores properties of Lie groups with special Randers metrics.

Contribution

It provides explicit formulas for flag curvature of invariant Randers metrics and analyzes conditions for constant positive curvature and Berwald type on Lie groups.

Findings

Explicit formula for flag curvature of invariant Randers metrics.

Characterization of Randers metrics with constant positive flag curvature.

Properties of Lie groups admitting special invariant Randers metrics.

Abstract

In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics on homogeneous spaces and, in special case, Lie groups. We then study Randers metrics of constant positive flag curvature and complete underlying Riemannian metric on Lie groups. Finally we give some properties of those Lie groups which admit a left invariant non-Riemannian Randers metric of Berwald type arising from a left invariant Riemannian metric and a left invariant vector field.