Abstract
The main purpose in this study is to create the adjoint curve of a curve according to the modified orthogonal frame created by torsion in Euclidean and Minkowski 3-space. Besides, it is another purpose to reveal the relationships between the modified orthogonal frame of these curves.In this paper, firstly, the adjoint curve of a space curve in 3D Euclidean space with respect to the modified orthogonal frame formed by torsion is defined and the modified orthogonal frame of the adjoint curve is given by a theorem in terms of the modified orthogonal frame of the main curve.With the help of this theorem, results about properties such as being a general helix and a Salkowski curve between main curve and adjoint curve were given. Similar approaches are discussed for non-null curves in 3D Minkowski space and the adjoint curve of a space curve is defined.
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