2015/03/10 by Tongzhu Li, Li, Tongzhu, Jie Qing +3 · 1 citation
Mathematics · #53A30 #53C40 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.DG #msc:53A30 #msc:53C40
paper · pdf · doi:10.48550/arxiv.1503.02914
45 pages. arXiv admin note: text overlap with arXiv:math/0512090 by other authors
arxiv created 2015/03/10 · openalex publication_date 2015/03/10 · arxiv updated 2015/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.