学術雑誌論文 Envelopes of legendre curves in the unit spherical bundle over the unit sphere

LI, Yanlin  ,  PEI, Donghe  ,  TAKAHASHI, Masatomo  ,  YU, Haiou

69 ( 2 )  , pp.631 - 653 , 2018-12-14 , Oxford University Press
ISSN:0033-5606
内容記述
In this paper, we introduce a one-parameter family of Legendre curves in the unit spherical bundle over the unit sphere and the curvature. We give the existence and uniqueness theorems for one-parameter families of spherical Legendre curves by using the curvatures. Then we define an envelope for the one-parameter family of Legendre curves in the unit spherical bundle. We also consider the parallel curves and evolutes of one-parameter families of Legendre curves in the unit spherical bundle and their envelopes. Moreover, we give relationships among one-parameter families of Legendre curves in the unit spherical bundle over the unit sphere and one-parameter families of Legendre curves in the unit tangent bundle over the Euclidean plane.
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