New Isothermic surfaces
Geometric Topology
2020-11-17 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2011.07941,
title = {New Isothermic surfaces},
author = {Armando M. V. Corro and Marcelo Lopes Ferro},
journal= {arXiv preprint arXiv:2011.07941},
year = {2020}
}