Bifurcation of constant mean curvature tori in Euclidean spheres

TL;DR

This paper demonstrates the existence of infinitely many non-congruent constant mean curvature tori in Euclidean spheres, which accumulate at a Clifford torus, using bifurcation theory.

Contribution

It introduces a bifurcation approach to find new CMC tori in spheres that are not congruent to known Clifford tori, expanding the understanding of CMC surface embeddings.

Findings

Existence of infinite sequences of non-congruent CMC tori

Sequences accumulate at a CMC Clifford torus

Application of bifurcation theory to geometric embeddings

Abstract

We use bifurcation theory to show the existence of infinite sequences isometric embeddings of tori with constant mean curvature (CMC) in Euclidean spheres that are not isometrically congruent to the CMC Clifford tori, and accumulating at some CMC Clifford torus.