2016•Journal of Mathematical and Computational ScienceRequires access

Corresponding developable ruled surfaces in Euclidean 3-space E3

Nassar Hassan Abdel-All, Fathi M. Hamdoon, H.N. Abd-Ellah, A.K. Omran

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Abstract

In this paper, motion of Darboux vector on two different space curves in Euclidean 3-space is investigated. The structure of the motion is based on ruled surfaces generated by Darboux vector ~ ω. According to this, developability of the considered ruled surfaces are studied. An extensive comparison between these developable ruled surfaces is performed. Some relations between the corresponding curves on the developable ruled surfaces are performed. Finally, special correspondence is given and plotted.

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What this paper is about

In this paper, motion of Darboux vector on two different space curves in Euclidean 3-space is investigated. The structure of the motion is based on ruled surfaces generated by Darboux vector ~ ω. According to this, developability of the considered ruled surfaces are studied. An extensive comparison between these developable ruled surfaces is performed. Some relations between the corresponding curves on the developable ruled surfaces are performed. Finally, special correspondence is given and plotted.

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Available abstract

In this paper, motion of Darboux vector on two different space curves in Euclidean 3-space is investigated. The structure of the motion is based on ruled surfaces generated by Darboux vector ~ ω. According to this, developability of the considered ruled surfaces are studied. An extensive comparison between these developable ruled surfaces is performed. Some relations between the corresponding curves on the developable ruled surfaces are performed. Finally, special correspondence is given and plotted.

Key concepts: Developable surface, Ruled surface, Mathematics, Euclidean geometry, Space (punctuation), Motion (physics), Euclidean space, Pure mathematics

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