The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space

Preprint Series # 777
Izumiya, Shyuichi and Romero Fuster, Maria del Carmen The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space. (2006);

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Abstract

We introduce the notion of the lightcone Gauss-Kronecker curvature for a spacelike submanifold of codimention two in Minkowski space which is a generalization of the ordinary notion of Gauss curvature of hypersurfaces in Euclidean space. In the local sense, this curvature describes the contact of such submanifolds with lightlike hyperplanes. We study geometric properties of such curvatures and show a Gauss-Bonnet type theorem. As examples we have hypersurfaces in hyperbolic space, spacelike hypersurfaces in the lightcone and spacelike hypersurfaces in de Sitter space.

Item Type: Preprint 50 lightcone Gauss map, lightlike Gauss-Kronecker curvature, Gauss-Bonnet Theorem 53-xx DIFFERENTIAL GEOMETRY 1519