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 language | English |
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Pages (from-to) | 249-294 |
Number of pages | 46 |
Journal | Advances in Mathematics |
Volume | 311 |
DOIs | |
Publication status | Published - 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