Covariant description of isothermic surfaces
General Relativity and Quantum Cosmology
2020-02-26 v2
Abstract
We present a covariant formulation of the Gauss-Weingarten equations and the Gauss-Mainardi-Codazzi equations for surfaces in 3-dimensional curved spaces. We derive a coordinate invariant condition on the first and second fundamental form which is locally necessary and sufficient for the surface to be isothermic. We show how to construct isothermic coordinates.
Cite
@article{arxiv.1410.4526,
title = {Covariant description of isothermic surfaces},
author = {Jacek Tafel},
journal= {arXiv preprint arXiv:1410.4526},
year = {2020}
}
Comments
11 pages