2010/06/07 by Rabah Souam, Souam, Rabah, Joeri Van der Veken +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1006.1261
openalex publication_date 2010/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that a Riemannian product of type M x R (where R denotes the\nEuclidean line) admits totally umbilical hypersurfaces if and only if M has\nlocally the structure of a warped product and we give a complete description of\nthe totally umbilical hypersurfaces in this case. Moreover, we give a necessary\nand sufficient condition under which a Riemannian three-manifold carrying a\nunit Killing field admits totally geodesic surfaces and we study local and\nglobal properties of three-manifolds satisfying this condition.\n