Abstract
This chapter gives a brief introduction to classical isothermic immersions in Euclidean space, a notion easily extended to immersions of surfaces into each of the space forms. The definition, which is the existence of coordinate charts that are isothermal and whose coordinate curves are lines of curvature, seems more analytic than geometric. We show that CMC immersions are isothermic away from their umbilics, which indicates that isothermic immersions are generalizations of CMC immersions. The Christoffel transform provides geometric content to the concept.
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Jensen, G.R., Musso, E., Nicolodi, L. (2016). Isothermic Immersions. In: Surfaces in Classical Geometries. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-27076-0_9
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DOI: https://doi.org/10.1007/978-3-319-27076-0_9
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