Second order geometry of spacelike surfaces in de Sitter 5-space

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 S5 1 by using the action of GL(2,R) X 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 LMN-ellipse. This ellipse gives information on the lightlike binormal directions and consequently about their associated asymptotic directions.