On General Spherically Symmetric Finsler Metrics

TL;DR

This paper investigates the curvature properties of general spherically symmetric Finsler metrics, establishing their semi C-reducibility and conditions for zero mean stretch curvature, advancing understanding of their geometric structure.

Contribution

It proves semi C-reducibility for all such metrics and characterizes when they have vanishing mean stretch curvature, providing new insights into their curvature properties.

Findings

All general spherically symmetric Finsler metrics are semi C-reducible.

Derived necessary and sufficient conditions for zero mean stretch curvature.

Enhanced understanding of curvature characteristics in Finsler geometry.

Abstract

In this paper, we study some non-Riemannian curvature properties of general spherically symmetric Finsler metrics. First, we prove that every general spherically symmetric Finsler metric is semi C-reducible. Then, we find the necessary and sufficient condition under which a general spherically symmetric Finsler metric has vanishing mean stretch curvature.