On Minkowskian Product Einstein-Finsler spaces

TL;DR

This paper investigates Minkowskian product Finsler manifolds, establishing conditions under which such manifolds are Einstein, specifically relating Ricci flatness and Einstein properties of the component manifolds.

Contribution

It proves that Minkowskian product Finsler manifolds are Einstein only if they are Ricci flat or both component manifolds are Einstein with identical scalar functions.

Findings

Minkowskian product Finsler manifolds are Einstein iff Ricci flat or both factors are Einstein with same scalar.

The paper characterizes Einstein conditions in Minkowskian product Finsler spaces.

Provides conditions linking the Einstein property of the product to its factors.

Abstract

In this paper we study the Minkowskian product Finsler manifolds. More precisely, we prove that if the Minkowskian product Finsler manifold is Einstein then either the product manifold is Ricci flat or both the quotient manifolds are Einstein with same scalar functions.