Title: Finiteness of Totally Geodesic Hypersurfaces in Negative Curvature
Abstract: There is a broad body of work devoted to proving theorems of the following form: spaces with infinitely many special sub-spaces are either nonexistent or rare. Such finiteness statements are important in algebraic geometry, number theory, and the theory of moduli space and locally symmetric spaces. I will talk about joint work with Simion Filip and David Fisher proving a finiteness statement of this kind in a differential geometry setting. Our main theorem is that a closed negatively curved analytic Riemannian manifold with infinitely many totally geodesic hypersurfaces must be isometric to an arithmetic hyperbolic manifold.
Bryna Kra
(847) 491-5567
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