Intrinsic versus extrinsic geometry of Finsler surfaces

speaker: Sergei Ivanov (Steklov Institute of Mathematics at St.Petersburg)

abstract: By Gauss' Theorema Egregium, the intrinsic metric of of a surface in the Euclidean 3-space determines its extrinsic Gauss curvature. In particular it determines whether the second fundamental form at a point is of elliptic, hyperbolic, or parabolic type. These three types are affine invariant and they make sense for surfaces in non-Euclidean normed 3-spaces. This suggests the following question: Given two isometric embeddings of a Finsler 2-manifold into Minkowski 3-spaces, do they necessarily have the same type of the second fundamental form at a given point? I will show that the answer is affirmative for a certain class of Finsler metrics. (In general, the question remains open.)

timetable:
Mon 21 May, 9:10 - 10:00, Aula Dini
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