Finsler manifolds with Positive Weighted Flag Curvature
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916798055579648 |
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| author | Shen, Zhongmin Zhao, Runzhong |
| author_facet | Shen, Zhongmin Zhao, Runzhong |
| contents | The flag curvature is a natural Finsler extension of the sectional curvature in Riemannian geometry. However, there are many non-Riemannian quantities which interact with the flag curvature. In this paper, we introduce a notion of weighted flag curvature by modifying the flag curvature using the non-Riemannian quantity, $T$-curvature. We show that a forward complete open Finsler manifold with positive weighted flag curvature is necessarily diffeomorphic to the Euclidean space, and that a compact Finsler manifold with nonnegative weighted flag curvature and strictly convex boundary is diffeomorphic to a Euclidean ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06414 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finsler manifolds with Positive Weighted Flag Curvature Shen, Zhongmin Zhao, Runzhong Differential Geometry The flag curvature is a natural Finsler extension of the sectional curvature in Riemannian geometry. However, there are many non-Riemannian quantities which interact with the flag curvature. In this paper, we introduce a notion of weighted flag curvature by modifying the flag curvature using the non-Riemannian quantity, $T$-curvature. We show that a forward complete open Finsler manifold with positive weighted flag curvature is necessarily diffeomorphic to the Euclidean space, and that a compact Finsler manifold with nonnegative weighted flag curvature and strictly convex boundary is diffeomorphic to a Euclidean ball. |
| title | Finsler manifolds with Positive Weighted Flag Curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2303.06414 |