Spacelike surfaces in anti de Sitter four-space from a contact viewpoint |
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Authors: | Shyuichi Izumiya Donghe Pei María del Carmen Romero Fuster |
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Institution: | 1.Department of Mathematics,Hokkaido University,Sapporo,Japan;2.School of Mathematics and Statistics,Northeast Normal University,Changchun,P.R. China;3.Departament de Geometría i Topología, Facultat de Matemàtiques,Universitat de València,Burjassot (València),Spain |
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Abstract: | We define the notions of (S
t
1 × 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 which have geometric properties different from those of the above Gauss maps. As a consequence,
we can say that anti de Sitter space has much richer geometric properties than the other space forms such as Euclidean space,
hyperbolic space, Lorentz-Minkowski space and de Sitter space. |
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Keywords: | |
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