Anisotropic isoparametric hypersurfaces in Euclidean spaces

Jianquan Ge; Hui Ma

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arXiv · 1008.1926

Anisotropic isoparametric hypersurfaces in Euclidean spaces

Jianquan Ge·Hui Ma

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Abstract

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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Jianquan Ge, Hui Ma. 2010-08-11. Anisotropic isoparametric hypersurfaces in Euclidean spaces. https://arxiv.org/abs/1008.1926

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