Möbius curvature, Laguerre curvature and Dupin hypersurface

Tongzhu Li*, Jie Qing, Changping Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)249-294
Number of pages46
JournalAdvances in Mathematics
Volume311
DOIs
Publication statusPublished - 30 Apr 2017

Keywords

  • Codazzi tensors
  • Dupin hypersurfaces
  • Isoparametric tensors
  • Laguerre curvatures
  • Möbius curvatures

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Li, T., Qing, J., & Wang, C. (2017). Möbius curvature, Laguerre curvature and Dupin hypersurface. Advances in Mathematics, 311, 249-294. https://doi.org/10.1016/j.aim.2017.02.024