Pairs of foliations on timelike surfaces in the de Sitter space S^3_1
Preprint Series # 920
Izumiya, Shyuichi and Tari, Farid Pairs of foliations on timelike surfaces in the de Sitter space S^3_1. (2008);
We define in this paper the asymptotic, characteristic and principal directions associated to the de Sitter Gauss map on a smooth timelike surface $M$ in the de Sitter space $S^3_1$. We study their properties and determine
the local topological configurations of their integral curves. These curves form pairs of foliations on some regions of $M$ and are defined in an analogous way to their classical contrepart on surfaces in the Euclidean 3-space. However, we show that their behaviour is distinct from that of their analogue on surface in the Euclidean 3-space.
|Uncontrolled Keywords:||Asymptotic curves, characteristic curves, lines of principal curvature, timelike surfaces, de Sitter Gauss map, singularities.|
|Subjects:||53-xx DIFFERENTIAL GEOMETRY|