Anisotropic isoparametric hypersurfaces in Euclidean spaces

Details Anisotropic isoparametric hypersurfaces in Euclidean spaces Anisotropic isoparametric hypersurfaces in Euclidean spaces

2010-08-11

arxiv.org/abs/1008.1926v2

Ann. Glob. Anal. Geom. 41(2012), 347-355

Mathematics

Differential Geometry

Scientific paper

In this note, we give a classification of complete anisotropic isoparametric hypersurfaces, i.e., hypersurfaces with constant anisotropic principal curvatures, in Euclidean spaces, which is in analogue with the classical case for isoparametric hypersurfaces in Euclidean spaces. On the other hand, by an example of local anisotropic isoparametric surface constructed by B. Palmer, we find that anisotropic isoparametric hypersurfaces have both local and global aspects as in the theory of proper Dupin hypersurfaces.

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