ON EINSTEIN (α,β )-METRICS

Document Type: Regular Paper

Authors

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

Abstract

– In this paper we consider some (α ,β ) -metrics such as generalized Kropina, Matsumoto and F (α β )2
α = + metrics, and obtain necessary and sufficient conditions for them to be Einstein metrics when β
is a constant Killing form. Then we prove with this assumption that the mentioned Einstein metrics must be
Riemannian or Ricci flat.

Keywords