The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space |
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Authors: | Shyuichi Izumiya María del Carmen Romero Fuster |
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Institution: | (1) Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan;(2) Departament de Geometria i Topologia, Universitat de València, 46100 Burjassot (València), Spain |
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Abstract: | We introduce the notion of the lightcone Gauss–Kronecker curvature for a spacelike submanifold of codimension 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. |
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Keywords: | 53C40 58K05 |
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