Spherically Symmetric Finsler Metrics With Constant Ricci And Flag Curvature

TL;DR

This paper investigates spherically symmetric Finsler metrics on R^n that exhibit both constant Ricci and flag curvature, expanding understanding of their geometric properties and classifications.

Contribution

It introduces a comprehensive study of spherically symmetric Finsler metrics with simultaneous constant Ricci and flag curvature, a topic less explored in prior research.

Findings

Characterization of spherically symmetric Finsler metrics with constant Ricci and flag curvature.

Identification of conditions under which such metrics exist.

Potential classification results for these metrics.

Abstract

Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically symmetric metrics with constant Ricci curvature and constant flag curvature.