Families of conformal tori of revolution in the 3-sphere

TL;DR

This paper constructs a family of conformal tori of revolution in the 3-sphere with varying numbers of bulges, using Darboux transformations, expanding the understanding of conformal geometry beyond constant mean curvature surfaces.

Contribution

It introduces a new family of conformal tori of revolution in the 3-sphere with n bulges, generated via Darboux transformations from constant mean curvature tori.

Findings

Constructed families for all positive integers n

Tori have n bulges and are conformal but not constant mean curvature

Method extends the class of known conformal tori in the 3-sphere

Abstract

For all positive integers n we construct a 1-parameter family of conformal tori of revolution in the 3-sphere with n bulges. These tori arise by Darboux transformations of constant mean curvature tori but do not have constant mean curvature in the 3-sphere.