2024/11/15 by Alex Moriani, Moriani, Alex, Enrico Trebeschi +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.2411.10352
openalex publication_date 2024/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study in this article the curvature of complete maximal spacelike submanifolds in pseudo-hyperbolic spaces. We show that the scalar curvature of these submanifolds is nonpositive in every signature. This gives, together with a result of Ishihara, a sharp bound on the scalar curvature of complete maximal spacelike submanifolds in pseudo-hyperbolic spaces of every signature. We show that achieving the bound at a point is equivalent to achieving it identically, and explicitely describe the submanifolds achieving the bound. When the codimension is equal to 1, we deduce a sharp upper bound on the Ricci curvature of complete maximal hypersurfaces in Anti-de Sitter spaces, and characterize the hypersurfaces achieving it. Finally, we discuss the link between scalar curvature and Gromov-hyperbolicity for complete maximal spacelike submanifolds in pseudo-hyperbolic spaces.