Evolutes of framed immersions in the Euclidean space

Honda, Shun'ichi; Takahashi, Masatomo

Hokkaido University Preprint Series in Mathematics, 2016, 1095, 1-24

Permalink : https://doi.org/10.14943/84239

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DOI	https://doi.org/10.14943/84239
URI	https://hdl.handle.net/2115/69899
タイトル	Evolutes of framed immersions in the Euclidean space
著者	著者名 Honda, Shun'ichi
著者	著者名 Takahashi, Masatomo
言語	英語
発行日	2016-09-12
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1095
ページ	1-24
抄録	We consider a smooth curve with singular points in the Euclidean space. As a smooth curve with singular points, we have introduced a framed curve or a framed immersion. A framed immersion is a smooth curve with a moving frame and the pair is an immersion. We consider an evolute and a focal surface of a framed immersion in the Euclidean space. The evolutes and focal surfaces of framed immersions are generalizations of each object in the case of a regular space curve. We investigate relationships between singularities of the evolutes and of the focal surfaces. Moreover, we give properties of the evolutes and repeated evolutes.
資源タイプ	紀要論文
出版タイプ	Version of Record