Index of bipolar surfaces to Otsuki tori

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 ${\tilde{O}}_{p/q}$ 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.

16 pages, v2: improved structure and exposition

References in corpus (1)

• Laplacian eigenvalues functionals and metric deformations on compact manifolds

Cited by in corpus (1)

• On the Index of Fraser-Sargent-type minimal surfaces