Differential Geometry Working Seminar

Anton Ilianshenko, Department of Pure Mathematics, University of Waterloo

"Riemannian Submersions, Part II"

This is the second talk on Riemannian Submersions. In the first talk we considered the local viewpoint by introducing the O’Neil tensors and used them to get identities for the curvature of the total space in terms of the base and the fibers. In this talk we switch to the global theory. In particular, assuming completeness of the total space we will prove that a Riemannian submersion is a locally trivial fiber bundle. Next, we will focus on the case with totally geodesic fibers, which has a very interesting family of examples.

This seminar will be held jointly online and in person:

• Zoom link: https://uwaterloo.zoom.us/j/95873618652?pwd=OENSeFdERzUzV2NkM3hjQ0F1MzFYUT09
• Room: MC 5403