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Bertrand and Mannheim curves of framed curves in the 3-dimensional Euclidean space

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/89248

Title: Bertrand and Mannheim curves of framed curves in the 3-dimensional Euclidean space
Authors: Honda, Shun'ichi Browse this author
Takahashi, Masatomo Browse this author
Issue Date: 20-May-2019
Publisher: Department of Mathematics, Hokkaido University
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1126
Start Page: 1
End Page: 18
Abstract: A Bertrand curve is a special class of space curves that the principal normal line of the curve and the principal normal line of another curve are the same. On the other hand, a Mannheim curve is also a special class of space curves that the principal normal line of the curve and the bi-normal line of another curve are the same. By definitions, the other curves are parallel curves to the direction of the principal normal vector. Even if regular cases, the existence conditions of the Bertrand and Mannheim curves seem to be wrong. Moreover, parallel curves may have singular points. As smooth curves with singular points, we consider framed curves in the Euclidean space. Then we define Bertrand and Mannheim curves of framed curves. Moreover, we clarify the Bertrand and Mannheim curves are depend of the moving frame.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/74203
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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