On Riemann curvature of spherically symmetric metrics

S. G. Elgendi

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arXiv · 2407.03855

On Riemann curvature of spherically symmetric metrics

S. G. Elgendi

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Abstract

In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct a Berwald frame for a spherically symmetric Finsler surface and calculate some associated geometric objects. Several examples are provided and discussed. Finally, we give a note on a certain general $(\alpha,\beta)$-metric that appears in the literature.

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S. G. Elgendi. 2024-07-04. On Riemann curvature of spherically symmetric metrics. https://arxiv.org/abs/2407.03855

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