Mannheim Offsets of Ruled Surfaces

Keziban Orbay, Emin Kasap, İsmail Aydemir
2009 Mathematical Problems in Engineering  
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
more » ... ffset of developable ruled surface is constant distance from it. Finally, examples are also given.
doi:10.1155/2009/160917 fatcat:jiwlcxa42rgcnabpmzu7m6sypq