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.
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
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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