||Involutes of fronts in the Euclidean plane
FUKUNAGA, TomonoriTAKAHASHI, Masatomo
Beiträge zur Algebra und Geometrie = Contributions to Algebra and Geometry
653 , 2016-09 , Springer
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