Journal for Geometry and Graphics 24 (2020), No. 2, 257--267
Copyright Heldermann Verlag 2020
Ruled Surface Generated by a Curve Lying on a Regular Surface and its Characterizations
Soukaina Ouarab
Dept. of Mathematics and Computer Science, Ben M’Sik Faculty of Sciences, Hassan II University, Casablanca, Morocco
soukaina.ouarab.sma@gmail.com
Amina Ouazzani Chahdi
Dept. of Mathematics and Computer Science, Ben M’Sik Faculty of Sciences, Hassan II University, Casablanca, Morocco
ouazzaniamina@hotmail.com
Malika Izid
Dept. of Mathematics and Computer Science, Ben M’Sik Faculty of Sciences, Hassan II University, Casablanca, Morocco
izid.malika@gmail.com
We construct and study special ruled surfaces, whose rulings are linear combinations of Darboux frame vectors of its base curve relative to an arbitrary regular surface in euclidean 3-space. We give the relationship between both Darboux frames of the common curve relative to the two surfaces, and investigate different properties of the constructed ruled surface. Moreover, we presente three examples with illustrations in the real euclidean 3-space.
Keywords: Ruled surface, Darboux frame, striction curve, Gaussian curvature, mean curvature, Euclidean 3-space.
MSC: 53A05
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