On Kropina transformation of exponential (α,β)-metrics

Zohrehvand, Mosayeb; Fasihi-Ramandi, Ghodratallah; Azami, Shahroud

doi:10.22098/jfga.2024.14680.1117

On Kropina transformation of exponential (α,β)-metrics

Document Type : Original Article

Authors

¹ Department of Mathematical Science and Statistics, Malayer University, Malayer, Iran

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

10.22098/jfga.2024.14680.1117

Abstract

In this paper‎, ‎we study the Kropina transformation of exponential (α,β)-metric F=α\exp(s), s:=β/α‎. ‎We characterize the conditions under which this class of (α,β)-metric is locally projectively flat‎, ‎locally dually flat‎, ‎and Douglas metric‎. ‎Based on‎, ‎we show that the Kropina transformation of an exponential (α,β)-metric is locally projectively flat‎, ‎locally dually flat and Douglas metric if and only if the exponential (α,β)-metric is locally projectively flat‎, ‎locally dually flat and Douglas metric‎, ‎respectively.

Keywords

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