On conformally related general (alpha, beta)-metric with a closed and conformal 1-form

Subject Areas : Statistics

Ghorban Ghasemi ¹ , Abolfazl Behzadi ²

1 - Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran
2 - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Received: 2018-01-03 Accepted : 2024-05-13 Published : 2024-01-18

Keywords: Finsler geometry, General (alpha, beta)-metric, Conformally related, Douglas curvature.,

Abstract :

Abstract A manifold equipped with a Finsler metric is called Finsler manifold. Finsler metrics must satisfy in Smoothness, Positive homogeneity and Strong convexity condition. There are a class of Finsler metrics that calculation is easier where are called $ (alpha,beta) $ -metrics. In this paper, we investigate conformally transformations of general $ (alpha,beta) $ -metrics where $ beta $ is a closed and conformal 1-form. These metrics are a generalization of $ (alpha,beta) $ -metrics and spherically symmetric metrics. Finsler metrics whose Douglas curvature tensor vanish, are called Douglas metrics. We first defin $ b^2 $ -conformally related metrics. Then we obtain the necessary and sufficient condition to be invariant under the conformal transformations, i.e. let $ F $ is Douglas Finsler metric and for $ b^2 $ -conformally related metrics $ F $ and $ \bar{F} $ , we find necessary and sufficient condition to $ \bar{F} $ be Douglas type.

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