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Hokkaido University Preprint Series in Mathematics >
Legendre curves in the unit spherical bundle and evolutes
| Title: | Legendre curves in the unit spherical bundle and evolutes |
| Authors: | Takahashi, Masatomo Browse this author |
| Issue Date: | 19-Jun-2015 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1071 |
| Start Page: | 1 |
| End Page: | 19 |
| Abstract: | In order to consider singular curves in the unit sphere, we consider Legendre curves in the unit spherical bundle. By using a moving frame, we de ne the curvature of Legendre curves in the unit spherical bundle. As applications, we give a relationship among Legendre curves in the unit spherical bundle, Legendre curves in the unit tangent bundle and framed curves in the Euclidean space, respectively. Moreover, we de ne not only an evolute of a front, but also an evolute of a frontal in the unit sphere under certain conditions. Since the evolute of a front is also a front, we can take evolute again. On the other hand, the evolute of a frontal if exists, is also a frontal. We give an existence and uniqueness conditions of the evolute of a frontal. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69875 |
| 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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