Topological and geometric rigidity of nonnegatively curved submanifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929715238928384 |
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| author | Vlachos, Theodoros |
| author_facet | Vlachos, Theodoros |
| contents | We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We show that this condition imposes strong constraints on either the topology or geometry of the submanifold. Additionally, we provide examples that demonstrate the sharpness of our result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological and geometric rigidity of nonnegatively curved submanifolds Vlachos, Theodoros Differential Geometry 53C20, 53C40, 53C42 We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We show that this condition imposes strong constraints on either the topology or geometry of the submanifold. Additionally, we provide examples that demonstrate the sharpness of our result. |
| title | Topological and geometric rigidity of nonnegatively curved submanifolds |
| topic | Differential Geometry 53C20, 53C40, 53C42 |
| url | https://arxiv.org/abs/2502.09630 |