Constant curvature hypersurfaces of cylinders over space forms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909857038204928 |
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| author | Carvalho, Arnando Tojeiro, Ruy |
| author_facet | Carvalho, Arnando Tojeiro, Ruy |
| contents | We classify the hypersurfaces of dimension n >= 3 with constant sectional curvature in the product spaces R^k x S^{n-k+1} and R^k x H^{n-k+1}, for 2 <= k <= n-1. Our results provide a complete description of these hypersurfaces and extend previous classifications of constant curvature submanifolds in product spaces of space forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constant curvature hypersurfaces of cylinders over space forms Carvalho, Arnando Tojeiro, Ruy Differential Geometry 53B25 We classify the hypersurfaces of dimension n >= 3 with constant sectional curvature in the product spaces R^k x S^{n-k+1} and R^k x H^{n-k+1}, for 2 <= k <= n-1. Our results provide a complete description of these hypersurfaces and extend previous classifications of constant curvature submanifolds in product spaces of space forms. |
| title | Constant curvature hypersurfaces of cylinders over space forms |
| topic | Differential Geometry 53B25 |
| url | https://arxiv.org/abs/2510.17030 |