Position vectors and characterization of curves in the isotropic space

This thesis consists of three parts. In the first chapter, the problem of expressing the position vector of the curve in terms of curvature and torsion functions is investigated in Euclidean space. This problem is not solved for general curves in Euclidean space, but it is solved for some special curves. In the second part, basic definitions and theorems about Euclidean space and isotropic space are given. In the third chapter, the position vector of a curve in isotropic space is expressed in terms of curvature and torsion. Finally, position vectors and graphs of some special curves in isotropic space are given.