Conformally Flat Hypersurfaces of E4 |
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| Authors: | F. Defever U. Hertrich-Jeromin |
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| Affiliation: | (1) Departement Wiskunde Ku Leuven, Zuivere En Toegepaste Differentiaalmeetkunde, Celestijnenlaan 200 B, 3001 Heverlee (Leuven), Belgium;(2) Arbeitsgruppe Geometrie Fachbereich Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany |
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| Abstract: | We consider 3-dimensional conformally flat hypersurfaces of E4 with 2 different principal curvatures such that the coordinate directions are principal directions. We describe explicitly those which allow an immersion with constant mean curvature. They are shown to be in close correspondence with solutions of the nonlinear integrable sine-Gordon and sinh-Gordon equations. Conversely, this provides a geometrical characterization for this particular class of conformally flat hypersurfaces of E4. |
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