Möbius and Laguerre geometry of Dupin Hypersurfaces
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Möbius and Laguerre geometry of Dupin Hypersurfaces

  • Author(s): Li, T
  • Qing, J
  • Wang, C
  • et al.
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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