On the Mannheim Surface Offsets

Details On the Mannheim Surface Offsets On the Mannheim Surface Offsets

2011-10-05

arxiv.org/abs/1110.0916v1

Mathematics

Differential Geometry

13 pages. arXiv admin note: substantial text overlap with arXiv:1108.4535 and arXiv:1108.6076

Scientific paper

In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider the ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic trihedron(dual Darboux frame). We obtain the relationships between the invariants of Mannheim ruled surfaces. Furthermore, we give the conditions for these surface offset to be developable.

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