Envelopes of Legendre Curves in the Unit Tangent Bundle over the Euclidean Plane
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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.
Journal
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- Results in Mathematics
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Results in Mathematics 71 (3-4), 1473-1489, 2017-06
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Details
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- CRID
- 1050001201687260288
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- NII Article ID
- 120006529865
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- NII Book ID
- AA12502442
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- ISSN
- 14209012
- 14226383
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- HANDLE
- 10258/00009214
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- Crossref
- CiNii Articles
- KAKEN