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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 →KAKEN DB | | Romero Fuster, Maria del Carmen Browse this author |
| Keywords: | Lightcone Gauss map | | lightlike Gauss | | Kronecker curvature | | Gauss–Bonnet theorem |
| Issue Date: | Mar-2007 |
| Publisher: | Birkhäuser Basel (Springer Science+Business Media) |
| Journal Title: | Selecta Mathematica, New Series |
| Volume: | 13 |
| Issue: | 1 |
| Start Page: | 23 |
| End Page: | 55 |
| Publisher DOI: | 10.1007/s00029-007-0033-9 |
| 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. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/28202 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 泉屋 周一
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