Covariant description of isothermic surfaces
arXiv:1410.4526 · doi:10.1016/S0034-4877(17)30010-1
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.
11 pages