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arXiv · 2006.10352

Properties of Berwald scalar curvature

Ming Li·Lihong Zhang
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Abstract

In this short paper, we prove that a Finsler manifold with vanishing Berwald scalar curvature has zero $\mathbf{E}$-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. This improves a previous result in \cite{Li}. For $(\alpha,\beta)$-metrics on manifold of dimension greater than 2, if the mean Landsberg curvature and the Berwald scalar curvature both vanish, the Berwald curvature also vanishes.

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Ming Li, Lihong Zhang. 2020-06-18. Properties of Berwald scalar curvature. https://doi.org/10.1007/s11464-020-0872-7

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