open access

https://doi.org/10.14943/84233

https://hdl.handle.net/2115/69893

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

英語

2016-05-12

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

1089

1-15

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.

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