Möbius and Laguerre geometry of Dupin Hypersurfaces
Skip to main content
eScholarship
Open Access Publications from the University of California

Möbius and Laguerre geometry of Dupin Hypersurfaces

  • Author(s): Li, Tongzhu
  • Qing, Jie
  • Wang, Changping
  • 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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View