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Graduate Student Geometry-Topology Seminar

Monday, February 20, 2017 - 3:15pm

Joseph Hoisington

University of Pennsylvania


University of Pennsylvania


We will explore the properties of totally geodesic maps, those which map the geodesics of one manifold to geodesics of another.  We will prove a factorization theorem: Any totally geodesic map is the composition of a Riemannian submersion with totally geodesic fibers with a totally geodesic immersion of the base.  To better understand this theorem, we will also talk about several other simple but important theorems for totally geodesic Riemannian submersions.