Involutes of fronts in the Euclidean plane
type: Item
instance of: scholarly article
title: Involutes of fronts in the Euclidean plane
zbMATH Open document ID: 1352.58007
author: Tomonori Fukunaga
author: Masatomo Takahashi
published in: Beiträge zur Algebra und Geometrie
publication date: 2016-08-25T00:00:00Z
full work available at URL: http://hdl.handle.net/10258/00009010
review text: 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.
reviewed by: Aleksandr G. Aleksandrov
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 57R45
zbMATH DE Number: 6619594
zbMATH Keywords: real plane curves
zbMATH Keywords: evolutes
zbMATH Keywords: involutes
zbMATH Keywords: evolvents
zbMATH Keywords: wave fronts
zbMATH Keywords: inflection points
zbMATH Keywords: curvature
zbMATH Keywords: Legendre immersion
describes a project that uses: CandS
MaRDI profile type: Publication
OpenAlex ID: W2281799305
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DOI: 10.1007/S13366-015-0275-1
description: scientific article; zbMATH DE number 6619594