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# Spacelike surfaces in Anti de Sitter four-space from a contact viewpoint

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 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