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Research Article | Open Access

Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space

Wei Zhang1,3, Pengcheng Li2, Donghe Pei1( )
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
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Abstract

In the present paper, we defined the circular evolutes and involutes for a given spacelike framed curve with respect to Bishop directions in Minkowski 3-space. Then, we studied the essential duality relations among parallel curves, normal surfaces, and circular evolutes and involutes. Furthermore, we also studied the duality relations of their singularities. Based on these studies, we found that it is crucially important to consider the duality relations among different geometric objects for the research of submanifolds with singularities.

Keywords

spacelike framed curvescircular evolutesinvolutesparallel curvesnormal surfaces
CLC number: 53A04, 53A05, 57R45

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 5688-5707
DOI: 10.3934/math.2024276

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Cite this article:
Zhang W, Li P, Pei D. Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space. AIMS Mathematics, 2024, 9(3): 5688-5707. https://doi.org/10.3934/math.2024276

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Received: 30 December 2023
Revised: 16 January 2024
Accepted: 19 January 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)