Korean J. Math.  Vol 24, No 4 (2016)  pp.613-626
DOI: https://doi.org/10.11568/kjm.2016.24.4.613

Studying on a skew ruled surface by using the geodesic Frenet trihedron of its generator

Fathi M. Hamdoon, A. K. Omran

Abstract


In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator.  We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, minimal, II-minimal and Weingarten surface.  Moreover, the  parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.

Keywords


Ruled surfaces, Geodesic Frenet trihedron, Geodesic and Asymptotic lines.

Subject classification

53A04, 53A05.

Sponsor(s)



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References


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