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Envelopes of Legendre curves in the unit tangent bundle over the Euclidean plane
| Title: | Envelopes of Legendre curves in the unit tangent bundle over the Euclidean plane |
| Authors: | Takahashi, Masatomo Browse this author |
| Issue Date: | 12-May-2016 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1089 |
| Start Page: | 1 |
| End Page: | 15 |
| Abstract: | For singular plane curves, the classical definitions of envelopes are vague. In order to define envelopes for singular plane curves, we introduce a one-parameter family of Legendre curves in the unit tangent bundle over the Euclidean plane and the curvature. Then we give a definition of an envelope for the one-parameter family of Legendre curves. We investigate properties of the envelopes. For instance, the envelope is also a Legendre curve. Moreover, we consider bi-Legendre curves and give a relationship between envelopes. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69893 |
| 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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