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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.04495 |
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| _version_ | 1866917189654675456 |
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| author | Xia, Wei Zhong, Chunping |
| author_facet | Xia, Wei Zhong, Chunping |
| contents | Let $F: T^{1,0}M\rightarrow[0,+\infty)$ be a strongly convex complex Finsler metric on a complex manifold $M$ and $\pmb{J}$ the canonical complex structure on the complex manifold $T^{1,0}M$. We give a geometric characterization of strongly convex Kähler-Berwald metrics. In particular, we prove that $\pmb{J}$ is horizontally parallel with respect to the Cartan connection iff $F$ is a Kähler-Berwald metric. We also prove that the Cartan connection and the Chern-Finsler connection associated to $F$ coincide iff $\pmb{J}$ is both horizontal and vertical parallel with respect to the Cartan connection. Based on these results, we give a rigidity theorem of strongly convex Kähler-Berwald metrics with constant holomorphic sectional curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04495 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterization of strongly convex Kähler-Berwald metrics Xia, Wei Zhong, Chunping Differential Geometry 53C60, 32Q99 Let $F: T^{1,0}M\rightarrow[0,+\infty)$ be a strongly convex complex Finsler metric on a complex manifold $M$ and $\pmb{J}$ the canonical complex structure on the complex manifold $T^{1,0}M$. We give a geometric characterization of strongly convex Kähler-Berwald metrics. In particular, we prove that $\pmb{J}$ is horizontally parallel with respect to the Cartan connection iff $F$ is a Kähler-Berwald metric. We also prove that the Cartan connection and the Chern-Finsler connection associated to $F$ coincide iff $\pmb{J}$ is both horizontal and vertical parallel with respect to the Cartan connection. Based on these results, we give a rigidity theorem of strongly convex Kähler-Berwald metrics with constant holomorphic sectional curvatures. |
| title | Characterization of strongly convex Kähler-Berwald metrics |
| topic | Differential Geometry 53C60, 32Q99 |
| url | https://arxiv.org/abs/2601.04495 |