Geometry & Topology Seminar: "Finsler submanifolds, from viewpoint of Chern connection"

Organizer: Xiang Tang

Host: Quo-Shin Chi

Abstract:  This talk is based on the author's recent work. We introduce the notions of the second fundamental form and mean curvature for Finsler submanifolds in terms of Chern connection, and establish the fundamental equations by means of moving frame for the hypersurface case. We provide the estimation of image radius for compact submanifold, and prove that there
exists no compact minimal submanifold in any complete noncompact and simply connected Finsler manifold with nonpositive flag curvature. We also characterize the Minkowski hyperplanes, Minkowski hyperspheres and Minkowski cylinders as the only hypersurfaces in Minkowski space with parallel second fundamental form.