Abstract
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.
Citation
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.
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