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arXiv · 1503.02914

M\"obius and Laguerre geometry of Dupin Hypersurfaces

Tongzhu Li·Jie Qing·Changping Wang
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Abstract

In this paper we show that a Dupin hypersurface with constant M\"{o}bius curvatures is M\"{o}bius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al on the classification of Dupin hypersurfaces.

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Tongzhu Li, Jie Qing, Changping Wang. 2015-03-10. M\"obius and Laguerre geometry of Dupin Hypersurfaces. https://arxiv.org/abs/1503.02914

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