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); AbstractWe 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 3space. However, we show that their behaviour is distinct from that of their analogue on surface in the Euclidean 3space. Item Type:  Preprint 

Uncontrolled Keywords:  Asymptotic curves, characteristic curves, lines of principal curvature, timelike surfaces, de Sitter Gauss map, singularities. 

Subjects:  53xx DIFFERENTIAL GEOMETRY 

ID Code:  1884 

