Evolutoids of the mixed-type curves
type: Item
instance of: scholarly article
title: Evolutoids of the mixed-type curves
zbMATH Open document ID: 1483.53015
DOI: 10.1155/2021/9330963
author: Xin Zhao
author: Donghe Pei
published in: Advances in Mathematical Physics
publication date: 2022-01-06T00:00:00Z
review text: Summary: The evolutoid of a regular curve in the Lorentz-Minkowski plane \(\mathbb{R}_1^2\) is the envelope of the lines between tangents and normals of the curve. It is regarded as the generalized caustic (evolute) of the curve. The evolutoid of a mixed-type curve has not been considered since the definition of the evolutoid at lightlike point can not be given naturally. In this paper, we devote ourselves to consider the evolutoids of the regular mixed-type curves in \(\mathbb{R}_1^2\). As the angle of lightlike vector and nonlightlike vector can not be defined, we introduce the evolutoids of the nonlightlike regular curves in \(\mathbb{R}_1^2\) and give the conception of the \(\sigma \)-transform first. On this basis, we define the evolutoids of the regular mixed-type curves by using a lightcone frame. Then, we study when does the evolutoid of a mixed-type curve have singular points and discuss the relationship of the type of the points of the mixed-type curve and the type of the points of its evolutoid.
Mathematics Subject Classification ID: 53A35
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 7452865
zbMATH Keywords: Lorentz-Minkowski plane
zbMATH Keywords: non-light-like regular curves
zbMATH Keywords: \(\sigma \)-transform
zbMATH Keywords: light-cone frame
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/9330963
OpenAlex ID: W4200133262
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description: scientific article; zbMATH DE number 7452865