Involutes of fronts in the Euclidean plane
The authors introduce a notion of involutes for curves with singular points in the Euclidean plane (that are called fronts), discuss some useful properties of evolutes and involutes of fronts without reflections points, investigate singular points of involutes of such fronts (cf. [\textit{V. I. Arnol'd}, Russ. Math. Surv. 33, No. 5, 99--116 (1978; Zbl 0415.58004)], establish a relationship between singular points of involutes of fronts and their vertices, etc. In particular, they show how evolutes and involutes of fronts without inflection points are related with the differential and the integral of the curvature of Legendre immersion, derive a formula for the \(n\)-th iteration of involutes of such fronts similarly to the case of evolutes (see [\textit{T. Fukunaga} and \textit{M. Takahashi}, J. Singul. 10, 92--107 (2014; Zbl 1308.53005)]), and so on.
scientific article; zbMATH DE number 6619594
scientific article