学術雑誌論文 Involutes of fronts in the Euclidean plane

FUKUNAGA, Tomonori  ,  TAKAHASHI, Masatomo

57 ( 3 )  , pp.637 - 653 , 2016-09 , Springer
ISSN:0138-48212191-0383
NII書誌ID(NCID):AA00558880
内容記述
For a regular plane curve, an involute of it is the trajectory described by the end of a stretched string unwinding from a point of the curve. Even for a regular curve, the involute always has a singularity. By using a moving frame along the front and the curvature of the Legendre immersion in the unit tangent bundle, we define an involute of the front in the Euclidean plane and give properties of it. We also consider a relationship between evolutes and involutes of fronts without inflection points. As a result, the evolutes and the involutes of fronts without inflection points are corresponding to the differential and the integral of the curvature of the Legendre immersion.
Mathematics Subject Classification : 58K05; 53A04; 57R45
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