论文标题
双极表面的索引
Index of bipolar surfaces to Otsuki tori
论文作者
论文摘要
对于（1/2，\ sqrt 2/2），对于每个有理数$ p/q \ $ p/q \，一个人可以在$ \ mathbb s^3 $中构造$ \ mathbb s^1 $ -equivariant minimal torus，称为otsuki torus，并由$ o_ {p/q/q} $表示。 Lawson的双极表面构造应用于$ o_ {p/q} $，给出了最小的圆环$ \ widetilde o_ {p/q} $，in $ \ mathbb s^4 $。在本文中，我们以$ p/q $接近$ \ sqrt 2/2 $的价格给出了摩尔斯指数上的上和下限。我们还陈述了有关一般情况的数值辅助猜想。
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.
