A characterization of Moebius isoparametric hypersurfaces of the sphere

摘要

We consider a proper, umbilic-free immersion of an n-dimensional manifold M in the sphere S n+1. We show that M is a Moebius isoparametric hypersurface if, and only if, it is a cyclide of Dupin or a Dupin hypersurface with constant Moebius curvature. Keywords Moebius isoparametric hypersurfaces - Dupin hypersurfaces - Constant Moebius curvature Mathematics Subject Classification (2000) 53A07 - 53A30 - 53C40 - 53C42 Communicated by D.V. Alekseevsky.