学術雑誌論文 Envelopes of Legendre Curves in the Unit Tangent Bundle over the Euclidean Plane

TAKAHASHI, Masatomo

71 ( 3-4 )  , pp.1473 - 1489 , 2017-06 , springer
ISSN:1422-63831420-9012
NII書誌ID(NCID):AA12502442
内容記述
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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