Jon Herman, Pure Mathematics Department, University of Waterloo
“Gauss’s Theorema Egregium”
This talk will be concerned with hypersurfaces in Euclidean space. The second fundamental form allows us to define a selfadjoint endomorphism on each tangent space, called the shape operator. From the shape operator we define the principal, Gaussian and mean curvatures. After introducing these notions I will give a proof of Gauss’s Theorema Egregium which asserts that the Gaussian curvature of a hypersurface in R3 is invariant under isometries.