|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Pairs of foliations on timelike surfaces in the de Sitter space S^3_1
| Title: | Pairs of foliations on timelike surfaces in the de Sitter space S^3_1 |
| Authors: | Izumiya, Shyuichi Browse this author | | Tari, Farid Browse this author |
| Keywords: | Asymptotic curves | | characteristic curves | | lines of principal curvature | | timelike surfaces | | de Sitter Gauss map | | singularities. |
| Issue Date: | 18-Jun-2008 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 920 |
| Start Page: | 1 |
| End Page: | 21 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69727 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
