Abstract
The aim of this paper is to define
 Bäcklund transformation between two timelike curves in four dimensional
 Minkowski space. For this purpose, we examine the transformation depending on
 the choice of rotation matrix which determines the relations between Frenet
 frames of timelike Bäcklund curves. There are three different cases for
 rotation matrix; two of them are spherical rotations on the spacelike hyperplane
 and one of them is hyperbolical rotation on the timelike hyperplane. For each
 case, we get the relations between curvature functions of timelike Bäcklund
 curves. By the way, we prove that timelike Bäcklund curves must have equal constant
 second torsion functions up to sign. This also means that Bäcklund
 transformation is a transformation which maps a timelike curve with constant
 second torsion to another timelike curve with constant second torsion.
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