Intrinsic Volumes on Pseudo-Riemannian Manifolds
Explore the theory of intrinsic volumes in pseudo-Riemannian geometry through this 30-minute lecture by Andreas Bernig from the Hausdorff Center for Mathematics. Delve into the extension of intrinsic volumes from Euclidean space to pseudo-Euclidean spaces and pseudo-Riemannian manifolds. Learn about the characterization of intrinsic volumes through Steiner's tube formula and Hadwiger's theorem, and discover how Weyl's principle applies in this context. Examine the natural analogues of fundamental results such as Hadwiger's theorem, Weyl's principle, and Crofton formulas on spheres in the pseudo-Riemannian setting. Gain insights into the collaborative work of Bernig, Dmitry Faifman, and Gil Solanes in developing this theory, which bridges classical differential geometry with modern pseudo-Riemannian concepts.