On a class of conformally flat (α,β)-metrics with special curvature properties

Document Type : Original Article

Author

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

Abstract

This paper is devoted to study of a class of conformally flat (α,β)-metrics that have of the form F = αexp(2s)/s; where s := β/α. They are called Kropina change of exponential (α,β)-metrics. We prove that if F has relatively isotropic mean Landsberg curvature or almost vanishing Xi-curvature then it is a Riemannian metric or a locally Minkowski metric. Also, we prove that, if F be a weak Einstein metric, then it is either a Riemannian metric or a locally Minkowski metric.

Keywords

References

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Journal of Finsler Geometry and its Applications
Volume 4, Issue 2
December 2023
Pages 1-21

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