Characterizations of some curves according to dual bishop frame in dual space

The differential geometry of curves is one of the most significant areas that are studied according to different frames in different spaces. Frenet frame which consists of the tangent, principal normal, and binormal vectors of a curve in 3-dimension Euclid Space is the best known ortonormal frame for study the differential geometry of this curve. Furthermore, the shape of a space curve, in other words, the local behaviour in space is completely determined by the curvature and torsion of this curve. Therefore, the curve must be continuously derivatiable up to at least 3rd order as a curve can be completely studied. There are also the other frames which have the same advantages as Frenet frame and can be compared with Frenet fame in studying of the curves. One of them is Bishop frame that is defined by Richard L. Bishop in 1975. This frame is a moving frame which is well-defined even when the curve has vanishing second derivative. Several studies about space curves by using Bishop frame did and various characterizations are given. Another space in which curves are studied is dual space . The curves in can be seen as natural expansion of the curves in Euclid space due to the fact that can be able to take into consideration as a 6-dimension reel space including 3-dimension Euclid space . So, some researchers have studied these curves by using dual Frenet and dual Bishop frames in dual space . In this study, some characterizations of dual general helices, dual slant helices, dual Darboux helices, and dual similar curves by using dual Bishop frame are studied. Also, dual spherical indicatrix curves according to dual Bishop frame are obtained with the help of dual Frenet frame of curves on dual unit sphere.