A remark on the reach and upper bounds on some extrinsic geometry invariants of submanifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912267332747264 |
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| author | Mirzaie, Reza |
| author_facet | Mirzaie, Reza |
| contents | We consider a compact submanifold $M$ of a Riemannian manifold $N$ and we use the second variation formula as a tool to drive some geometric results on reach$(M, N)$ the reach of $M$ in $N$, including some useful relations between the extrinsic geometry of $M$ in $N$ and reach$(M, N)$. Our results generalize some theorems previously proved for the special case where $N$ is Euclidean space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark on the reach and upper bounds on some extrinsic geometry invariants of submanifolds Mirzaie, Reza Differential Geometry 53C70, 53C22, 53B25, 62C20, 68U05 We consider a compact submanifold $M$ of a Riemannian manifold $N$ and we use the second variation formula as a tool to drive some geometric results on reach$(M, N)$ the reach of $M$ in $N$, including some useful relations between the extrinsic geometry of $M$ in $N$ and reach$(M, N)$. Our results generalize some theorems previously proved for the special case where $N$ is Euclidean space. |
| title | A remark on the reach and upper bounds on some extrinsic geometry invariants of submanifolds |
| topic | Differential Geometry 53C70, 53C22, 53B25, 62C20, 68U05 |
| url | https://arxiv.org/abs/2503.07054 |