Abstract—In differential geometry of curves and surfaces, a ruled surface represents one of the most fascinating topics in surface theory, it is defined by choosing a curve which called base curve and a line along that curve (ruling). An important number of researchers in many papers have studied one of the moving frames of its base curve.
In this paper, we consider Striction curve of a non-cylindrical ruled surface as base curve of the ruled surface whose rulings are linear combinations of Frenet frame vectors of the first ruled surface. We investigate some important characteristic properties of the new ruled surface such as the Gaussian curvature and the mean curvature. Moreover, we give characterizations relatively to its developability and minimality and achieve by giving an example with illustrations.

Index Terms—Ruled surface, Frenet frame, striction curve, Gaussian curvature, mean curvature.

The authors are with Ben M’sik Faculty of Sciences/Hassan II University of Casablanca, Casablanca, Morocco (email: soukaina.ouarab.sma@gmail.com).

Cite: Soukaina Ouarab, Amina Ouazzani Chahdi, "Some Characteristic Properties of Ruled Surface with Frenet Frame of an Arbitrary Non-cylindrical Ruled Surface in Euclidean 3-Space," International Journal of Applied Physics and Mathematics vol. 10, no. 1, pp. 16-24, 2020.

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