Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2111.00156 |
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Sommario:
- 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.