Spacelike surfaces in Anti de Sitter fourspace from a contact viewpoint
Preprint Series # 914 Izumiya, Shyuichi and Pei, Donghe and Romero Fuster, Maria del Carmen Spacelike surfaces in Anti de Sitter fourspace from a contact viewpoint. (2008); AbstractWe 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 4space. 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 GaussKronecker curvatures and show a GaussBonnet 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, LorentzMinkowski space and de Sitter space.
Item Type:  Preprint 

Additional Information:  40 

Uncontrolled Keywords:  Anti de Sitter
4space, $S_t^1¥times S_s^2$nullcone Legendrian Gauss map, $S_+^2$nullcone Lagrangian Gauss map, lightlike
hyperbolic cylinder 

Subjects:  53xx DIFFERENTIAL GEOMETRY 

ID Code:  1858 

