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

Chen, Liang; Takahashi, Masatomo

Hokkaido University Preprint Series in Mathematics, 2015, 1072, 1-27

Permalink : https://doi.org/10.14943/84216

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アクセス権	open access
DOI	https://doi.org/10.14943/84216
URI	https://hdl.handle.net/2115/69876
タイトル	Dualities and evolutes of fronts in hyperbolic 2-space and de Sitter 2-space
著者	著者名 Chen, Liang
著者	著者名 Takahashi, Masatomo
言語	英語
キーワード	evolute
	spacelike front
	timelike front
	hyperbolic 2-space
	de Sitter 2-space
発行日	2015-06-19
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1072
ページ	1-27
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record