Finiteness of totally geodesic hypersurfaces

Autor:	Filip, Simion, Fisher, David, Lowe, Ben
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Dynamical Systems Mathematics - Geometric Topology 37D20 37D40 53C20 11F06
Druh dokumentu:	Working Paper
Popis:	We prove that a closed negatively curved analytic Riemannian manifold that contains infinitely many totally geodesic hypersurfaces is isometric to an arithmetic hyperbolic manifold. Equivalently, any closed analytic Riemannian manifold with negative sectional curvature has only finitely many totally geodesic hypersurfaces, unless it has constant curvature. Comment: 30 pages, minor revisions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.03430 Zobrazit plný text záznamu View this record from Arxiv