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arXiv · 2408.03430

Finiteness of totally geodesic hypersurfaces

Simion Filip·David Fisher·Ben Lowe
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Abstract

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.

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Simion Filip, David Fisher, Ben Lowe. 2024-08-06. Finiteness of totally geodesic hypersurfaces. https://arxiv.org/abs/2408.03430

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