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On the dual Bishop Darboux rotation axis of the dual space curve. (English) Zbl 1171.53014

The authors introduce the dual version of the Bishop frame-off a space-curve in the three-dimensional space \(D^3\) over the ring \(D\) of dual numbers. Particularly, they determine the instantaneous dual Bishop Darboux rotation axis of a dual space curve and prove the decomposition of the dual Darboux rotation of a dual Bishop frame into two simultaneous rotations.

MSC:

53A25 Differential line geometry
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