A characterization of weakly Berwald spaces with (α,β)-metrics

Kun Wang,Chunping Zhong

doi:10.1016/j.difgeo.2022.101870

A characterization of weakly Berwald spaces with (α,β)-metrics

Kun Wang, Chunping Zhong

https://doi.org/10.1016/j.difgeo.2022.101870

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Journal: Differential Geometry and its Applications	Publication Date: Mar 7, 2022
Citations: 1

Affiliation: Guangzhou University, Xiamen University

#Smooth Manifold #Berwald Space + Show 1 more

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Abstract

Let F=αϕ(s),s=βα, be an (α,β)-metric on a smooth manifold M of dimension n≥3 such that ϕ(s) comes from a real analytic but not even function. In this paper we give a characterization of (M,F) to be a weakly Berwald space. More precisely, we prove that F has vanishing S-curvature if and only if F has vanishing E-curvature.

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