Dupin hypersurfaces with four principal curvatures, II
| dc.creator | Cecil, Thomas | |
| dc.creator | Chi, Quo-Shin | |
| dc.creator | Jensen, Gary | |
| dc.date | 2005-12-05 | |
| dc.date.accessioned | 2026-07-07T06:54:51Z | |
| dc.date.available | 2026-07-07T06:54:51Z | |
| dc.description | If $M$ is an isoparametric hypersurface in a sphere $S^n$ with four distrinct principal curvatures, then the principal curvatures $κ_1,...,κ_4$ can be ordered so that their multiplicities satisfy $m_1=m_2$ and $m_3=m_4$, and the cross-ratio $r$ of the principal curvatures (the Lie curvature) equals -1. In this paper, we prove that if $M$ is an irreducible connected proper Dupin hypersurface in $\R^n$ (or $S^n$) with four distinct principal curvatures with multiplicities $m_1=m_2 \geq 1$ and $m_3=m_4=1$, and constant Lie curvature $r=-1$, then $M$ is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the assumption of irreducibility is replaced by compactness and $r$ is merely assumed to be constant. | |
| dc.identifier | https://arxiv.org/abs/math/0512090 | |
| dc.identifier | http://arxiv.org/abs/math/0512090 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106085 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C40 | |
| dc.title | Dupin hypersurfaces with four principal curvatures, II | |
| dc.type | text |