Mathematical Sciences: Geometry of Surfaces in Lorentz Space

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Martin Magid will investigate timelike and spacelike surfaces in Lorentz space. The primary motivation for studying these surfaces comes from physics and the theory of general relativity. He intends to use the Gauss map to achieve a deeper understanding of these surfaces. Timelike surfaces can be used to construct spacetimes and to understand the geometry of spacetimes by providing lower dimensional examples. The Gauss map of a spacelike surface has its range in the Grassmannian of spacelike two dimensional planes in Lorentz space. Magid will investigate to what extent such a surface is determined by its Gauss map and which maps are Gauss maps. He will also consider surfaces for which the image of the Gauss map has constant curvature. His second project is concerned with the classification of timelike surfaces with zero mean curvature which are given as the graph of a function.