2007/06/11 by Gabriel Ruiz-Hernández, Gabriel Ruiz-Hernandez, Ruiz-Hernandez, Gabriel
Computer Science · Mathematics · #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.DG #msc:53C40 #msc:53C42
paper · pdf · doi:10.48550/arxiv.0706.1524
15 pages
arxiv created 2007/06/11 · openalex publication_date 2007/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by a Blaschke's work about analytic convex surfaces, we study \em shadow boundaries of Riemannian submanifolds M, which are defined by a parallel vector field along M. Since a shadow boundary is just a closed subset of M, first, we will give a condition that guarantee its smoothness. It depends on the second fundamental form of the submanifold. It is natural to search for what kind of properties might have such submanifolds of M? Could they be totally geodesic or minimal? Answers to these and related questions are given in this work.