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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 267, Pages 164–181
(Mi tm2597)
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This article is cited in 5 scientific papers (total in 5 papers)
Spacelike Surfaces in Anti de Sitter Four-Space from a Contact Viewpoint
S. Izumiyaa, D. Peib, M. C. Romero Fusterc a Department of Mathematics, Hokkaido University, Sapporo, Japan
b School of Mathematics and Statistics, Northeast Normal University, Changchun, P. R. China
c Departament de Geometría i Topología, Facultat de Matemàtiques, Universitat de València, Burjassot, València, Spain
Abstract:
We define the notions of $(S_\mathrm t^1\times S_\mathrm s^2)$-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.
Received in April 2009
Citation:
S. Izumiya, D. Pei, M. C. Romero Fuster, “Spacelike Surfaces in Anti de Sitter Four-Space from a Contact Viewpoint”, Singularities and applications, Collected papers, Trudy Mat. Inst. Steklova, 267, MAIK Nauka/Interperiodica, Moscow, 2009, 164–181; Proc. Steklov Inst. Math., 267 (2009), 156–173
Linking options:
https://www.mathnet.ru/eng/tm2597 https://www.mathnet.ru/eng/tm/v267/p164
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