On quasi-Eienstein Finsler spaces

TL;DR

This paper introduces the concept of quasi-Einstein metrics within Finsler geometry, establishing their relationship with solutions to the Finslerian Ricci flow and extending Ricci soliton ideas beyond Riemannian spaces.

Contribution

It defines quasi-Einstein Finsler metrics and proves their equivalence with solutions to the Finslerian Ricci flow in the compact case.

Findings

Quasi-Einstein Finsler metrics solve the Finslerian Ricci flow.

Certain Finsler Ricci flow solutions are quasi-Einstein metrics.

Extension of Ricci soliton concepts to Finsler geometry.

Abstract

The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces. Quasi-Einstein metrics serve also as solution to the Ricci flow equation. Here, the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined. In compact case, it is proved that the quasi-Einstein metrics are solution to the Finslerian Ricci flow and conversely, certain form of solutions to the Finslerian Ricci flow are quasi-Einstein Finsler metrics.