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.
Graduate Student Geometry-Topology Seminar
Monday, February 20, 2017 - 3:15pm
Joseph Hoisington
University of Pennsylvania