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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 MíSik Faculty of Sciences, Hassan II University, Casablanca, Morocco
soukaina.ouarab.sma@gmail.com

Amina Ouazzani Chahdi
Dept. of Mathematics and Computer Science, Ben MíSik Faculty of Sciences, Hassan II University, Casablanca, Morocco
ouazzaniamina@hotmail.com

Malika Izid
Dept. of Mathematics and Computer Science, Ben MíSik 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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