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arXiv · 2111.00156

Characterizations of complex Finsler Metrics

Hongjun Li·Hongchuan Xia
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Abstract

Munteanu defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold $(M,F)$. We first prove that the holomorphic sectional curvature tensors of the canonical connection coincide with those of the Chern-Finsler connection associated to $F$ if and only if $F$ is a Kähler-Finsler metric. We also investigate the relationship of the Ricci curvatures (resp. scalar curvatures) of these two connections when $M$ is compact. As an application, two characterizations of balanced complex Finsler metrics are given. Next, we obtain a sufficient and necessary condition for a balanced complex Finsler metric to be Kähler-Finsler. Finally, we investigate conformal transformations of a balanced complex Finsler metric.

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Hongjun Li, Hongchuan Xia. 2023-02-06. Characterizations of complex Finsler Metrics. https://doi.org/10.1007/s12220-023-01272-3

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