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Dualities and evolutes of fronts in hyperbolic 2-space and de Sitter 2-space

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84216

Title: Dualities and evolutes of fronts in hyperbolic 2-space and de Sitter 2-space
Authors: Chen, Liang Browse this author
Takahashi, Masatomo Browse this author
Keywords: evolute
spacelike front
timelike front
hyperbolic 2-space
de Sitter 2-space
Issue Date: 19-Jun-2015
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1072
Start Page: 1
End Page: 27
Abstract: We consider the differential geometry of evolutes of singular curves in hyperbolic 2- space and de Sitter 2-space. Firstly, as an application of the basic Legendrian duality theorems, we give the definitions of fronts in hyperbolic 2-space or de Sitter 2-space, respectively. We also give the notions of moving frames along the fronts. By using the moving frames, we define the evolutes of spacelike fronts and timelike fronts, and investigate the geometric properties of these evolutes. As results, these evolutes can be viewed as wavefronts from the viewpoint of Legendrian singularity theory. At last, we study the relationships among these evolutes.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69876
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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