Abstract
In the present paper, a new type of special curve couple which are called WC^{∗}-partner curves are introduced according to alternative moving frame {N,C,W}. The distance function between the corresponding points of reference curve and its partner curve is obtained. Besides, the angle function between the vector fields of alternative frame of the curves is expressed by means of alternative curvatures f and g. In addition to these, various characterizations are obtained related to these curves.
Highlights
The angle function between the vector ...elds of alternative frame of the curves is expressed by means of alternative curvatures f and g
The curves are the fundamental structure of di¤erential geometry
Two curves which have some special properties at their corresponding points are called curve pairs
Summary
The curves are the fundamental structure of di¤erential geometry. Numerous studies of curves are carried out in 3 dimensional Euclidean space. These curves are de...ned by Mannheim with the equality 2+ 2 = w2 =constant Another characterization can be made as two curves and in E3 which are called Manneim partner curves if the principal normal vector ...elds of coincide with the binormal vector ...elds of at the corresponding points of curves [5, 6, 12, 14]. This paper is expected to de...ne a new kind of curve pairs which are called W C partner curves and give various characterization of these curves. For this purpose, an alternative frame on original curve is used and another curve is de...ned using this frame. Afterwards, the de...nition and main characterizations corporated to distance function and angle function of W C partner curves are introduced
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