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# Pairs of foliations on timelike surfaces in the de Sitter space S^3_1

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 Please use this identifier to cite or link to this item:https://doi.org/10.14943/84069

 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

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