On a Class of Weakly Weighted Einstein Metrics

TL;DR

This paper investigates a broad class of weighted Ricci curvatures in Finsler geometry, focusing on Randers metrics with almost isotropic weighted Ricci curvatures, advancing understanding of curvature control in these spaces.

Contribution

It characterizes Randers metrics with almost isotropic weighted Ricci curvatures, expanding the theoretical framework of weighted Ricci curvatures in Finsler geometry.

Findings

Characterization of Randers metrics with almost isotropic weighted Ricci curvatures

Enhanced understanding of volume control in Finsler manifolds

Development of generalized weighted Ricci curvature concepts

Abstract

Weighted Ricci curvatures with various weights of the S-curvature have played an important role in Finsler geometry, especially in the control of volumes of Finsler manifolds. In this paper, we study general weighted Ricci curvatures, and characterize Randers metrics of almost isotropic weighted Ricci curvatures.