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Evolutes of framed immersions in the Euclidean space
| Title: | Evolutes of framed immersions in the Euclidean space |
| Authors: | Honda, Shun'ichi Browse this author | | Takahashi, Masatomo Browse this author |
| Issue Date: | 12-Sep-2016 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1095 |
| Start Page: | 1 |
| End Page: | 24 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69899 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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