Rigidity of riemannian manifolds containing an equator
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910757218680832 |
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| author | Mazet, Laurent |
| author_facet | Mazet, Laurent |
| contents | In this paper, we prove that a Riemannian $n$-manifold $M$ with sectional curvature bounded above by $1$ that contains a minimal $2$-sphere of area $4π$ which has index at least $n-2$ has constant sectional curvature $1$. The proof uses the construction of ancient mean curvature flows that flow out of a minimal submanifold. As a consequence we also prove a rigidity result for the Simon-Smith minimal spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_01994 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Rigidity of riemannian manifolds containing an equator Mazet, Laurent Differential Geometry In this paper, we prove that a Riemannian $n$-manifold $M$ with sectional curvature bounded above by $1$ that contains a minimal $2$-sphere of area $4π$ which has index at least $n-2$ has constant sectional curvature $1$. The proof uses the construction of ancient mean curvature flows that flow out of a minimal submanifold. As a consequence we also prove a rigidity result for the Simon-Smith minimal spheres. |
| title | Rigidity of riemannian manifolds containing an equator |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2010.01994 |