HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >

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

Files in This Item:
pre914.pdf302.24 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/84063

Title: Spacelike surfaces in Anti de Sitter four-space from a contact viewpoint
Authors: Izumiya, Shyuichi Browse this author
Pei, Donghe Browse this author
Romero Fuster,Maria del Carmen Browse this author
Keywords: Anti de Sitter 4-space
S1t × S2s-nullcone Legendrian Gauss map
S2+-nullcone Lagrangian Gauss map
lightlike hyperbolic cylinder
Issue Date: 7-May-2008
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 914
Start Page: 1
End Page: 20
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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69721
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University