Conformally closed weakly Berwald metrics

Document Type : Original Article

Authors

Akbar Tayebi

Faezeh Eslami

Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

10.22034/kjm.2023.389192.2801

Abstract

A weakly Berwald metric is called a conformally closed weakly Berwald metric if for any conformal change remains a weakly Berwald metric. In this paper, we study the conformally closed weakly Berwald metrics and find the necessary and sufficient condition under which a weakly Berwald metric be conformally closed. We show that a Randers metric is a conformally closed weakly Berwald metric if and only if it is a Riemannian metric or the conformal transformation is homothety.

Keywords

Conformal metrics

Berwald curvature

mean Berwald curvature

Subjects

• 53 Differential geometry

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