Index of bipolar surfaces to Otsuki tori
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916480280428544 |
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| author | Morozov, Egor |
| author_facet | Morozov, Egor |
| contents | For each rational number $p/q\in (1/2,\sqrt 2/2)$ one can construct an $\mathbb S^1$-equivariant minimal torus in $\mathbb S^3$ called Otsuki torus and denoted by $O_{p/q}$. The Lawson's bipolar surface construction applied to $O_{p/q}$ gives a minimal torus $\widetilde O_{p/q}$ in $\mathbb S^4$. In this paper we give upper and lower bounds on the Morse index and the nullity of these tori for $p/q$ close to $\sqrt 2/2$. We also state a numerically assisted conjecture concerning the general case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06008 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Index of bipolar surfaces to Otsuki tori Morozov, Egor Differential Geometry 53C42 For each rational number $p/q\in (1/2,\sqrt 2/2)$ one can construct an $\mathbb S^1$-equivariant minimal torus in $\mathbb S^3$ called Otsuki torus and denoted by $O_{p/q}$. The Lawson's bipolar surface construction applied to $O_{p/q}$ gives a minimal torus $\widetilde O_{p/q}$ in $\mathbb S^4$. In this paper we give upper and lower bounds on the Morse index and the nullity of these tori for $p/q$ close to $\sqrt 2/2$. We also state a numerically assisted conjecture concerning the general case. |
| title | Index of bipolar surfaces to Otsuki tori |
| topic | Differential Geometry 53C42 |
| url | https://arxiv.org/abs/2207.06008 |