PROJECTIVELY RELATED EINSTEIN FINSLER SPACES

Document Type: Regular Paper

Authors

Department of Mathematics and Computer Science of Amir-Kabir University, Tehran, I. R. of Iran

Abstract

The main objective of this paper is to find the necessary and sufficient condition of a given Finsler
metric to be Einstein in order to classify the Einstein Finsler metrics on a compact manifold. The considered
Einstein Finsler metric in the study describes all different kinds of Einstein metrics which are pointwise
projective to the given one. This study has resulted in the following theorem that needs the proof of three
prepositions. Let F be a Finsler metric (n > 2) projectively related to an Einstein non-projectively flat
Finsler metric F , then F is Einstein if and only if F = λ F whereλ is a constant. A Schur type lemma is
also proved.

Keywords