Rashad A. Abdel-Baky, Monia F. Naghi, "Sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-Space," WSEAS Transactions on Mathematics, vol. 19, pp. 581-588, 2020, DOI:10.37394/23206.2020.19.63
Rashad A. Abdel-Baky, Monia F. Naghi. Sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-Space.
WSEAS Transactions on Mathematics. 2020;19:581-588. 10.37394/23206.2020.19.63
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 19, 2020
Sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-Space
Authors: ,
Abstract: In this paper, we introduce the notion of sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-space E3. We also show that the parametric curves on these surfaces are lines of curvature. Then, we derive the necessary and sufficient condition for the sweeping surface to become a developable ruled surface. In particular, we analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding developable surfaces which possessing these curves as lines of curvature.
Keywords:
textbf Natural mate curve, Proffile curve, Developable surface. MSC (2000). 53A04, 53A05, 53A17.
Pages: 581-588 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 19, 2020, Art. #63 DOI: 10.37394/23206.2020.19.63
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