Welcome to the website of the seminar organized by the Differential Geometry groups of Università di Torino and Politecnico di Torino.
For any information, please send an e-mail to dgseminar.torino@gmail.com.
The talks will take place either at the Deparment of Mathematics "G. Peano" (Università di Torino) or at the Department of Mathematical Sciences "G.L. Lagrange" (Politecnico di Torino).
NEXT TALK
07/05/2026, 14.30, Aula 1, Deparment of Mathematics "G. Peano" , Università di Torino,
Submanifolds with small normal curvatures
Abstract: Recent works by M. Gromov, A. Petrunin, O. Chodosh, and C. Li deals with the question: Given a closed smooth manifold M, minimize the maximum normal curvatures among all immersions of M into (high-dimensional) Euclidean spaces, under the constraint that the image lies in a closed ball of radius one. Replacing this constraint with the condition that the (extrinsic) diameter is at most two, one arrives at a different, but still natural, question. The result I will present is a first step in the exploration of this new question, namely: For any immersed submanifold M with diameter at most two, the maximum normal curvature is at least one, and equality holds if and only if M is diffeomorphic to a sphere or (real/complex/quaternionic/octonionic) projective space, embedded either as an affine sphere, or as a "Veronese" variety. Time allowing, I will discuss: (1) a generalization to submanifolds of spheres and hyperbolic spaces, (2) the proof, which uses A. Schur's "Bow" Lemma and K. Sakamoto's classification of submanifolds with planar geodesics, and (3) natural open questions.
FORTHCOMING TALKS
28/05/2026, 11.30, Aula 1, Deparment of Mathematics "G. Peano" , Università di Torino, Dott. Jakob Dittmer.
25/06/2026, 14.30, Sala S, Deparment of Mathematics "G. Peano" , Università di Torino, Prof.ssa Catherine Searle.