New Isothermic surfaces

TL;DR

This paper introduces a novel method for constructing isothermic surfaces using Ribaucour transformations, resulting in new complete surfaces with diverse geometric properties and explicit solutions to the Calapso equation.

Contribution

It presents a new construction technique for isothermic surfaces based on Ribaucour transformations, including families with bubble and planar end features.

Findings

Generated a three-parameter family of complete isothermic surfaces.

Derived a one-parameter family with planar ends.

Provided explicit solutions to the Calapso equation.

Abstract

In this paper, we consider a method of constructing isothermic surfaces based on Ribaucour transformations. By applying the theory to the cylinder, we obtain a three-parameter family of complete isothermic surfaces that contains n-bubble surfaces inside and outside of the cylinder. In addition, we also obtain one-parameter family of complete isothermic surface with planar ends. Such family of isothermic surfaces do not have constant mean curvature. As aplication we obtain explicit solutions of the Calapso equation.