Dept. Math, Hokkaido Univ. EPrints Server

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

Preprint Series # 914
Izumiya, Shyuichi and Pei, Donghe and Romero Fuster, Maria del Carmen Spacelike surfaces in Anti de Sitter four-space from a contact viewpoint. (2008);

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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.

Item Type:Preprint
Additional Information:40
Uncontrolled Keywords:Anti de Sitter 4-space, $S_t^1¥times S_s^2$-nullcone Legendrian Gauss map, $S_+^2$-nullcone Lagrangian Gauss map, lightlike hyperbolic cylinder
Subjects:53-xx DIFFERENTIAL GEOMETRY
ID Code:1858