On the Class of Einstein Exponential-Type
Finsler Metrics

Akbar Tayebi

University of Qom, Department of Mathematics, Faculty of Science, Qom, Iran
E-mail: akbar.tayebi@gmail.com

Ali Nankali

University of Qom, Department of Mathematics, Faculty of Science, Qom, Iran
E-mail: ali.nankali2327@yahoo.com

Behzad Najafi

Amirkabir University, Department of Mathematics and Computer Sciences, Tehran, Iran
E-mail: behzad.najafi@aut.ac.ir

Received August 8, 2015, revised July 29, 2017.

Abstract

In this paper, a special class of Finsler metrics, the so-called (α, β)-
metrics, which are defined by F = αφ(s), where α is a Riemannian metric and β is a 1-form, is studied. First we show that the class of almost regular metrics obtained by Shen is Einstein if and only if it reduces to the class of Berwald metrics. In this case, the Riemannian metrics are Ricci-flat. Then we prove that an exponential metric is Einstein if and only if it is Ricci-flat.