On Conformally Flat G.R.C. of Exponential (α,β)-Metrics

Zohrehvand, Mosayeb; Azami, Shahroud; JAFARI, MEHDI

doi:10.22080/cjms.2026.30974.1804

On Conformally Flat G.R.C. of Exponential (α,β)-Metrics

Document Type : Research Articles

Authors

¹ Department of Mathematics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran

² Department of Pure Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran

³ Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran

10.22080/cjms.2026.30974.1804

Abstract

This paper is devoted to the study of generalized Randers change in a specific class of (α,β)-metrics of conformally flat type. These metrics are defined as F = αexp(β/α) + εβ, where ε ̸= 0 is a real constant, and are called the generalized Randers change(G.R.C.) of the exponential metric. We demonstrate that if F possesses a relatively isotropic mean Landsberg curvature, it must either be a Riemannian or a locally Minkowskian metric. Furthermore, if F is a non-Riemannian weak Einstein metric, it necessarily
reduces to a locally Minkowskian metric.

Keywords