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Mathematical Problems in Engineering
Volume 2009, Article ID 160917, 9 pages
Research Article

Mannheim Offsets of Ruled Surfaces

1Department of Mathematics, Education Faculty, Amasya University, 0 5189 Amasya, Turkey
2Department of Mathematics, Arts and Science Faculty, Ondokuz Mayis University, 55139 Samsun, Turkey

Received 25 November 2008; Accepted 12 February 2009

Academic Editor: Francesco Pellicano

Copyright © 2009 Keziban Orbay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.