Mathematics – Differential Geometry
Scientific paper
2012-01-30
Mathematics
Differential Geometry
16 pages. arXiv admin note: substantial text overlap with arXiv:1108.6076
Scientific paper
In this paper, we define the dual geodesic trihedron(dual Darboux frame) of a spacelike ruled surface. Then, we study Mannheim offsets of spacelike ruled surfaces in dual Lorentzian space by considering the E. Study Mapping. We represent the spacelike ruled surfaces by dual Lorentzian unit spherical curves and define the Mannheim offsets of the spacelike ruled surfaces by means of dual Darboux frame. We obtain the relationships between the invariants of Mannheim spacelike offset surfaces and offset angle, offset distance. Furthermore, we give the conditions for these surface offsets to be developable and show that if the reference surface is not a cone, then the Mannheim surface offsets are developable if and only if the striction lines are perpendicular.
Onder Mehmet
Uğurlu Hüseyin H.
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