Mannheim Offsets of Ruled Surfaces

By Keziban Orbay, Emin Kasap, I. Aydemir. 2009

71 citations recorded by the source corpus.

In a recent works Liu and Wang (2008; 2007) study the Mannheim partner curves in the three dimensional space. In this paper, we extend the theory of the Mannheim curves to ruled surfaces and define two ruled surfaces which are offset in the sense of Mannheim. It is shown that, every developable ruled surface have a Mannheim offset if and only if an equation should be satisfied between the geodesic curvature and the arc-length of spherical indicatrix of it. Moreover, we obtain that the Mannheim offset of developable ruled surface is constant distance from it. Finally, examples are also given.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/20f3d0c431c2aa4e7563a003809470e4359ce94b

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Keziban Orbay
Emin Kasap

Citations in the corpus

On Mannheim partner curves in E 3 (2009, background): “In recent works, Liu and Wang (2007, 2008) are curious about the Mannheim curves in both Euclidean and Minkowski 3-space and they obtained the necessary and sufficient conditions between the curvature and the torsion for a curve to be the Mannheim partner curves.”