Invariant Matsumoto metrics on homogeneous spaces

TL;DR

This paper investigates invariant Matsumoto metrics on homogeneous spaces, deriving their flag curvature formulas, exploring special cases like naturally reductive spaces, and providing examples of geodesically complete spaces.

Contribution

It introduces explicit formulas for flag curvature of invariant Matsumoto metrics and analyzes special cases on homogeneous spaces, including naturally reductive and bi-invariant metrics.

Findings

Derived flag curvature formulas for invariant Matsumoto metrics.

Analyzed special cases like naturally reductive spaces.

Provided examples of geodesically complete Matsumoto spaces.

Abstract

In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces then we give the flag curvature formula of them. Also we study the special cases of naturally reductive spaces and bi-invariant metrics. We end the article by giving some examples of geodesically complete Matsumoto spaces.