2015/03/11 by Rosa Chaves, Chaves, Rosa, Eliane Pereira dos Santos +3
Mathematics · Physics and Astronomy · #53B20 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B20 #msc:53C42
paper · pdf · doi:10.48550/arxiv.1503.03507
28 pages
arxiv created 2015/03/11 · openalex publication_date 2015/03/11 · arxiv updated 2015/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we classify the hypersurfaces in \mathbbSn× ℝ and ℍn×ℝ, n≠ 3, with g distinct constant principal curvatures, g∈\1,2,3\, where \mathbbSn and ℍn denote the sphere and hyperbolic space of dimension n, respectively. We prove that such hypersurfaces are isoparametric in those spaces. Furthermore, we find a necessary and sufficient condition for an isoparametric hypersurface in \mathbbSn× ℝ⊂ ℝn+2 and ℍn×ℝ⊂ \mathbbLn+2 with flat normal bundle, having constant principal curvatures.