Open Access
2015 Second order geometry of spacelike surfaces in de Sitter 5-space
Masaki Kasedou, Ana Claudia Nabarro, Maria Aparecida Soares Ruas
Publ. Mat. 59(2): 449-477 (2015).


The de Sitter space is known as a Lorentz space with positive constant curvature in the Minkowski space. A surface with a Riemannian metric is called a spacelike surface. In this work we investigate properties of the second order geometry of spacelike surfaces in de Sitter space $S_1^5$ by using the action of $GL(2,\mathbb R)\times SO(1,2)$ on the system of conics defined by the second fundamental form. The main results are the classification of the second fundamental mapping and the description of the possible configurations of the $\mathit{LMN}$-ellipse. This ellipse gives information on the lightlike binormal directions and consequently about their associated asymptotic directions.


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Masaki Kasedou. Ana Claudia Nabarro. Maria Aparecida Soares Ruas. "Second order geometry of spacelike surfaces in de Sitter 5-space." Publ. Mat. 59 (2) 449 - 477, 2015.


Published: 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1327.53015
MathSciNet: MR3374614

Primary: 53A35 , 53B30

Keywords: asymptotic directions , de Sitter $5$-space , lightlike binormal directions , second order geometry , spacelike surface

Rights: Copyright © 2015 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.59 • No. 2 • 2015
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