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

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Published: Dec 30, 2016
Keywords:
Ruled surfaces, Geodesic Frenet trihedron, Geodesic and Asymptotic lines.
Mathematics Subject Classification:
53A04, 53A05.

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Fathi M. Hamdoon
Department of Mathematics Faculty of Science Al-Azhar University Assuit branch, Assiut 71524, Egypt.
A. K. Omran
Department of Mathematics Faculty of Science Al-Azhar University Assuit branch, Assiut 71524, Egypt.

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.


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References

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