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Isothermic and S-Willmore Surfaces as Solutions to a Problem of Blaschke

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Abstract

We consider the generalization of a classical problem of Blaschke to the higher codimensional case, characterizing Darboux pairs of isothermic surfaces and dual S-Willmore surfaces as the only non-trivial surface pairs that envelop a 2-sphere congruence and conformally correspond to each other. When the sphere congruence consists of the mean curvature spheres of one enveloping surface f, f must be a CMC-1 surface in hyperbolic 3-space, or an S-Willmore surface.

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  1. Fachbereich Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, D-10623, Berlin, Germany

    Xiang Ma

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  1. Xiang Ma
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Ma, X. Isothermic and S-Willmore Surfaces as Solutions to a Problem of Blaschke. Results. Math. 48, 301–309 (2005). https://doi.org/10.1007/BF03323370

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