Hypersurfaces with Constant Mean Curvatures on Finsler manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913263493578752 |
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| author | Chen, Yali He, Qun Qian, Yantong |
| author_facet | Chen, Yali He, Qun Qian, Yantong |
| contents | In this paper, we give the geometric meaning of hypersurfaces with constant mean curvature in a Finsler manifold by using volume preserving variation. Then we give the correspondence between principal curvatures of submanifolds by a homothetic navigation, which means that some geometric properties of submanifolds are the same. Finally, we deduce a Heintze-Karcher type inequality and prove an Alexandrov type theorem in special Finsler spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_09712 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hypersurfaces with Constant Mean Curvatures on Finsler manifolds Chen, Yali He, Qun Qian, Yantong Differential Geometry 53C60, 53C42, 34D23 In this paper, we give the geometric meaning of hypersurfaces with constant mean curvature in a Finsler manifold by using volume preserving variation. Then we give the correspondence between principal curvatures of submanifolds by a homothetic navigation, which means that some geometric properties of submanifolds are the same. Finally, we deduce a Heintze-Karcher type inequality and prove an Alexandrov type theorem in special Finsler spaces. |
| title | Hypersurfaces with Constant Mean Curvatures on Finsler manifolds |
| topic | Differential Geometry 53C60, 53C42, 34D23 |
| url | https://arxiv.org/abs/2203.09712 |