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Legendre curves in the unit spherical bundle and evolutes

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84215

Title: Legendre curves in the unit spherical bundle and evolutes
Authors: Takahashi, Masatomo Browse this author
Issue Date: 19-Jun-2015
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

Submitter: 数学紀要登録作業用

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