The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on December 1, 2015 at 14:00 in Room 478 of IMI.

A talk on:

Lorentz Surfaces in Four-dimensional Pseudo-Euclidean Spaces

will be delivered by Yana Aleksieva.

Everybody is invited.

Abstract. We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce canonical parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations.