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Research Article | Open Access

Singularities of swept surfaces in Euclidean 3-space

Fatemah Mofarreh1, Rashad A. Abdel-Baky2( )
Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia
Department of Mathematics, Faculty of Science, University of Assiut, 71516 Assiut, Egypt
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Abstract

This study examines the local singularities of tube surfaces, especially those of swept surfaces (SS) in Euclidean 3-space E3. SS is created by moving a planar curve through space such that the trajectory of any point on the surface remains perpendicular to the plane. The Type-2 Bishop frame is considered, and the singularities of these SS are analyzed. Examples are offered and illustrated.

Keywords

unfolding theorydevelopable surfaceBishop height function
CLC number: 53A04, 53A05, 53A17

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 26049-26064
DOI: 10.3934/math.20241272

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Cite this article:
Mofarreh F, Abdel-Baky RA. Singularities of swept surfaces in Euclidean 3-space. AIMS Mathematics, 2024, 9(9): 26049-26064. https://doi.org/10.3934/math.20241272

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Received: 20 April 2024
Revised: 24 July 2024
Accepted: 01 August 2024
Published: 15 September 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)