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Envelopes of Legendre curves in the unit tangent bundle over the Euclidean plane

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84233

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
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

Submitter: 数学紀要登録作業用

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