The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 14, 2014 at 14:00 in Room 478 of IMI.

A talk on:

„Surfaces with Lightlike Mean Curvature Vector Field in Four-dimensional Pseudo-Euclidean Spaces”

will be delivered by Velichka Milousheva, IMI - BAS.

Everybody is invited.

Abstract.

We consider surfaces in four-dimensional pseudo-Euclidean spaces with the property that the mean curvature vector is lightlike at each point. We introduce a geometrically determined moving frame field at each point of such a surface and using the derivative formulas for this frame field we obtain a system of invariant functions satisfying some integrability conditions. Our main theorem states that these invariants determine the surface up to a motion. We find examples of surfaces with lightlike mean curvature vector field in the class of the meridian surfaces of elliptic, hyperbolic or parabolic type.