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

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

Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 30 March 2024

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