On special type-2 Bishop motion and Bishop Darboux rotation axes of the space curve

Abstract

We have given a generalization of one parameter special Frenet motion to type-2 Bishop motion in Euclidean 3-space $$E^3$$ . Type-2 Bishop motion have been defined for space curve $$\beta $$ and then type-2 Bishop Darboux vector of this motion has been calculated for fixed and moving spaces in $$E^3$$ . Also, we have showed that type-2 Bishop rotation for space curves is decomposed into two simultaneous rotations. One of the axes of this simultaneous rotations is a parallel of the binormal vector of the curve, the other is the direction of the type-2 Bishop Darboux vector of the curve.