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Hokkaido University Preprint Series in Mathematics >
Spacelike surfaces in Anti de Sitter four-space from a contact viewpoint
| Title: | Spacelike surfaces in Anti de Sitter four-space from a contact viewpoint |
| Authors: | Izumiya, Shyuichi Browse this author | | Pei, Donghe Browse this author | | Romero Fuster, Maria del Carmen Browse this author |
| Keywords: | Anti de Sitter 4-space | | S1t × S2s-nullcone Legendrian Gauss map | | S2+-nullcone Lagrangian Gauss map | | lightlike hyperbolic cylinder |
| Issue Date: | 7-May-2008 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 914 |
| Start Page: | 1 |
| End Page: | 20 |
| Abstract: | We define the notions of $S_t^1¥times S_s^2$-nullcone Legendrian Gauss maps and $S^2_+$-nullcone Lagrangian Gauss maps on spacelike surfaces in Anti de Sitter 4-space. We investigate the relationships between singularities of these maps and geometric properties of surfaces as an application of the theory of Legendrian/Lagrangian singularities. By using $S^2_+$-nullcone Lagrangian Gauss maps, we define the notion of $S^2_+$-nullcone Gauss-Kronecker curvatures and show a Gauss-Bonnet type theorem as a global property. We also introduce the notion of horospherical Gauss maps whch has different geometric properties of the above Gauss maps. As a consequence, we can say that Anti de Sitter space has much more rich geometric properties than the other space forms such as Euclidean space, Hyperbolic space, Lorentz-Minkowski space and de Sitter space. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69721 |
| 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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