On a class of Einstein Finsler metrics

TL;DR

This paper investigates a specific class of Finsler metrics called general (,eta)-metrics, constructed from a Riemannian metric and a 1-form, focusing on those with constant Ricci curvature.

Contribution

It introduces new constructions of general (,eta)-metrics that possess constant Ricci curvature, expanding the understanding of their geometric properties.

Findings

Constructed new examples of (,eta)-metrics with constant Ricci curvature

Provided methods to generate such metrics from given Riemannian metrics and 1-forms

Enhanced the classification of Finsler metrics with special curvature properties

Abstract

In this paper, we study a class of Finsler metrics called general (\alpha,\beta)-metrics, which are defined by a Riemannian metric and an 1-form. We construct some general (\alpha,\beta)-metrics with constant Ricci curvature.