2012/01/01 by Erasmo Caponio
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Convexity #Curvature #Economics #Engineering #Geometric Analysis and Curvature Flows #Geometry #Hypersurface #Infinitesimal #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Point processes and geometric inequalities #Pseudo-Riemannian manifold #Pure mathematics #Ricci curvature #Riemannian manifold #math.DG #msc:53C22 #msc:53C60 #msc:58E10
paper · pdf · doi:10.1007/978-1-4614-4897-6_6
published as Springer Proceedings in Mathematics & Statistics, 26, 2013, pp. 163--177, ISBN:978-1-4614-4896-9 · 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition corrected
openalex publication_date 2012/01/01 · arxiv created 2012/04/19 · arxiv updated 2016/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.