On the index of minimal 2-tori in the 4-sphere
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866911877414518784 |
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| author | Kusner, Rob Wang, Peng |
| author_facet | Kusner, Rob Wang, Peng |
| contents | In this note we prove that any minimal $2$-torus in $S^4$ has Morse index at least $6$, with equality if and only if it is congruent to the Clifford torus in some great $S^3\subset S^4$.For a minimal $2$-torus in $S^n$ with vanishing Hopf differential, we show that its index is at least $n+3$, and that this estimate is sharp: the equilateral $2$-torus fully embedded in $S^5\subset S^n$ as a homogeneous minimal surface in $S^n$ has index exactly $n+3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_01615 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the index of minimal 2-tori in the 4-sphere Kusner, Rob Wang, Peng Differential Geometry 53A10 In this note we prove that any minimal $2$-torus in $S^4$ has Morse index at least $6$, with equality if and only if it is congruent to the Clifford torus in some great $S^3\subset S^4$.For a minimal $2$-torus in $S^n$ with vanishing Hopf differential, we show that its index is at least $n+3$, and that this estimate is sharp: the equilateral $2$-torus fully embedded in $S^5\subset S^n$ as a homogeneous minimal surface in $S^n$ has index exactly $n+3$. |
| title | On the index of minimal 2-tori in the 4-sphere |
| topic | Differential Geometry 53A10 |
| url | https://arxiv.org/abs/1803.01615 |