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arXiv · 2207.06008

Index of bipolar surfaces to Otsuki tori

Egor Morozov
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Abstract

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.

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Egor Morozov. 2022-07-13. Index of bipolar surfaces to Otsuki tori. https://doi.org/10.1007/s11040-024-09494-9

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