Geometry working seminar

Tuesday, September 30, 2014 1:00 pm - 1:00 pm EDT (GMT -04:00)

Jon Herman, Pure Mathematics Department, University of Waterloo

“The second fundamental form”

When an immersed submanifold of a Riemannian manifold is endowed with the induced metric it is called a Riemannian submanifold. The second fundamental form gives a way to compare the structure of a Riemannian manifold to a Riemannian submanifold. After introducing the second fundamental form, I will show how it gives a relationship between the Riemannian connections (via the Gauss formula), curvatures (via the Gauss equation) and geodesic curvatures (via the Gauss formula along a curve) of a Riemannian manifold and its Riemannian submanifolds.