On the Second Approximate Matsumoto Metric

TL;DR

This paper investigates the second approximate Matsumoto metric, establishing conditions under which it exhibits scalar flag curvature and isotropic S-curvature, linking these properties to isotropic Berwald metrics with almost isotropic flag curvature.

Contribution

It provides a characterization of the second approximate Matsumoto metric's curvature properties, connecting scalar flag curvature and isotropic S-curvature to Berwald metrics.

Findings

F has scalar flag curvature and isotropic S-curvature if and only if it is an isotropic Berwald metric

The metric exhibits almost isotropic flag curvature under these conditions

The study advances understanding of curvature conditions in Finsler geometry

Abstract

In this paper, we study the second approximate Matsumoto metric on a manifold M. We prove that F is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.