open access

https://doi.org/10.14943/84063

https://hdl.handle.net/2115/69721

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

英語

lightlike hyperbolic cylinder

2008-05-07

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

914

1-20

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.

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