Möbius and Laguerre geometry of Dupin Hypersurfaces

Abstract

In this paper we show that a Dupin hypersurface with constant Möbius curvatures is Möbius 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.

45 pages. arXiv admin note: text overlap with arXiv:math/0512090 by other authors

References in corpus (1)

• Laguerre Geometry of Hypersurfaces in ${\mathbb{R}}^n$