Isothermic and S-Willmore Surfaces as Solutions to Blaschke's Problem

Details Isothermic and S-Willmore Surfaces as Solutions to Blaschke's Problem Isothermic and S-Willmore Surfaces as Solutions to Blaschke's Problem

2004-05-05

arxiv.org/abs/math/0405085v1

ResultsMath.48:301-309,2005

Mathematics

Differential Geometry

11 pages

Scientific paper

We consider the generalization of classical Blaschke's Problem to higher codimension case, characterizing Darboux pair 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 is the mean curvature spheres of one envelop surface, it must be a cmc-1 surface in hyperbolic 3-space, or a S-Willmore surface. A study of conformally immersed surface pairs is indicated with discussion on the geometric meaning of new invariants.

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