Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane

In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="double-struck">R</...

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Autores principales:	Xin Zhao, Donghe Pei
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	pedal curve mixed-type curve lightlike point Lorentz–Minkowski plane Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6f577548fab343478590c9f9824c734a
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spelling	oai:doaj.org-article:6f577548fab343478590c9f9824c734a2021-11-25T18:16:33ZPedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane10.3390/math92228522227-7390https://doaj.org/article/6f577548fab343478590c9f9824c734a2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2852https://doaj.org/toc/2227-7390In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="double-struck">R</mi><mn>1</mn><mn>2</mn></msubsup></semantics></math></inline-formula>. The pedal curve is always given by the pseudo-orthogonal projection of a fixed point on the tangent lines of the base curve. For a mixed-type curve, the pedal curve at lightlike points cannot always be defined. Herein, we investigate when the pedal curves of a mixed-type curve can be defined and define the pedal curves of the mixed-type curve using the lightcone frame. Then, we consider when the pedal curves of the mixed-type curve have singular points. We also investigate the relationship of the type of the points on the pedal curves and the type of the points on the base curve.Xin ZhaoDonghe PeiMDPI AGarticlepedal curvemixed-type curvelightlike pointLorentz–Minkowski planeMathematicsQA1-939ENMathematics, Vol 9, Iss 2852, p 2852 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	pedal curve mixed-type curve lightlike point Lorentz–Minkowski plane Mathematics QA1-939
spellingShingle	pedal curve mixed-type curve lightlike point Lorentz–Minkowski plane Mathematics QA1-939 Xin Zhao Donghe Pei Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane
description	In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="double-struck">R</mi><mn>1</mn><mn>2</mn></msubsup></semantics></math></inline-formula>. The pedal curve is always given by the pseudo-orthogonal projection of a fixed point on the tangent lines of the base curve. For a mixed-type curve, the pedal curve at lightlike points cannot always be defined. Herein, we investigate when the pedal curves of a mixed-type curve can be defined and define the pedal curves of the mixed-type curve using the lightcone frame. Then, we consider when the pedal curves of the mixed-type curve have singular points. We also investigate the relationship of the type of the points on the pedal curves and the type of the points on the base curve.
format	article
author	Xin Zhao Donghe Pei
author_facet	Xin Zhao Donghe Pei
author_sort	Xin Zhao
title	Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane
title_short	Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane
title_full	Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane
title_fullStr	Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane
title_full_unstemmed	Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane
title_sort	pedal curves of the mixed-type curves in the lorentz-minkowski plane
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/6f577548fab343478590c9f9824c734a
work_keys_str_mv	AT xinzhao pedalcurvesofthemixedtypecurvesinthelorentzminkowskiplane AT donghepei pedalcurvesofthemixedtypecurvesinthelorentzminkowskiplane
_version_	1718411387662761984

Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane

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