Generalized P-Reducible Finsler Metrics

TL;DR

This paper introduces a broader class of Finsler metrics called generalized P-reducible metrics, explores their properties under scalar flag curvature, and extends classical results relating C-reducibility and P-reducibility.

Contribution

It generalizes Matsumotos theorem to a wider class of Finsler metrics and establishes conditions for these metrics to be C-reducible.

Findings

Generalized P-reducible metrics with scalar flag curvature can reduce to C-reducible metrics under certain conditions.

Such metrics with vanishing stretch curvature are shown to be C-reducible.

The work extends classical theorems in Finsler geometry to a broader context.

Abstract

In this paper, we study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metrics. This generalize Matsumotos theorem, which describes the equivalency of C-reducibility and P-reducibility on Finsler manifolds with scalar curvature. Then we show that generalized P-reducible metrics with vanishing stretch curvature are C-reducible.