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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:http://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
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

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