Mannheim Offsets of Ruled Surfaces

Keziban Orbay, Emin Kasap and İsmail Aydemir

Mathematical Problems in Engineering, 2009, vol. 2009, 1-9

Abstract:

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:160917

DOI: 10.1155/2009/160917

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