Index of Bipolar Surfaces to Otsuki Tori

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-13 DOI:10.1007/s11040-024-09494-9

Egor Morozov

引用次数: 0

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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双极表面到大月鸟迹的索引

对于每一个有理数（p/q 在 (1/2,\sqrt{2}/2)），我们都可以在（\mathbb {S}^1\）中构造一个 \(\mathbb {S}^3\)-后变的最小环，称为大月环，用 \(O_{p/q}\) 表示。将劳森双极面构造应用于 \(O_{p/q}/)可以得到 \(\mathbb {S}^4\) 中的最小环 \(\widetilde{O}_{p/q}/)。本文给出了 p/q 接近（（sqrt{2}/2）时这些环的莫尔斯指数和无效性的上下限。我们还提出了一个关于一般情况的数值猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

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