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Spacelike Parallels and Evolutes in Minkowski pseudo-spheres

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83917

Title: Spacelike Parallels and Evolutes in Minkowski pseudo-spheres
Authors: Izumiya, Shyuichi Browse this author
Takahashi, Masatomo Browse this author
Keywords: spacelike parallels
evolutes
caustics
Lagrangian singularities
Legendrian singularities
Issue Date: 23-Jan-2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 767
Start Page: 1
End Page: 39
Abstract: We consider extrinsic differential geometry on spacelike hypersurfaces in Minkowski pseudo-spheres (hyperbolic space, de Sitter space and the lightcone). In the previous paper we have shown a basic Legendrian duality theorem between pseudo-spheres. We define the spacelike parallels by using the basic Legendrian duality theorem. This definition unifies the notions of parallels of spacelike hypersurfaces in pseudo-spheres. We also define the evolute as the locus of singularities of the spacelike parallels. These notions are investigated as applications of Lagrangian or Legendrian singularity theory. We consider geometric properties of non-singular spacelike hypersurfaces corresponding to singularities of spacelike parallels or evolutes.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69575
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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