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Hokkaido University Preprint Series in Mathematics >
The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space
| Title: | The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space |
| Authors: | Izumiya, Shyuichi Browse this author | | Romero Fuster, Maria del Carmen Browse this author |
| Keywords: | lightcone Gauss map | | lightlike Gauss-Kronecker curvature | | Gauss-Bonnet Theorem |
| Issue Date: | 1-Apr-2006 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 777 |
| Start Page: | 1 |
| End Page: | 31 |
| 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69585 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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