Singularities of swept surfaces in Euclidean 3-space

Fatemah Mofarreh; Rashad A. Abdel-Baky; Fatemah Mofarreh; Rashad A. Abdel-Baky

doi:10.3934/math.20241272

AIMS Mathematics

2024, Volume 9, Issue 9: 26049-26064. doi: 10.3934/math.20241272

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Singularities of swept surfaces in Euclidean 3-space

Fatemah Mofarreh ¹,
Rashad A. Abdel-Baky ^{2
,
,}

1.
Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Assiut, 71516 Assiut, Egypt

Received: 20 April 2024 Revised: 24 July 2024 Accepted: 01 August 2024 Published: 09 September 2024
MSC : 53A04, 53A05, 53A17

This study examines the local singularities of tube surfaces, especially those of swept surfaces $ (SS) $ in Euclidean 3-space $ \mathcal{E}^{3} $. $ 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.
- unfolding theory,
- developable surface,
- Bishop height function
Citation: Fatemah Mofarreh, Rashad A. Abdel-Baky. Singularities of swept surfaces in Euclidean 3-space[J]. AIMS Mathematics, 2024, 9(9): 26049-26064. doi: 10.3934/math.20241272

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Abstract

This study examines the local singularities of tube surfaces, especially those of swept surfaces $ (SS) $ in Euclidean 3-space $ \mathcal{E}^{3} $. $ 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.

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