Notes on Mannheim curves in Euclidean space

This thesis consists of four chapters. In the first chapter is devoted to the introduction. In the second chapter, basic concepts and definitions about curves in the Euclidean space are introduced. In the third chapter, Mannheim curves and Mannheim partner curves according to Frenet frame in 3-dimensional Euclidean space are defined and the characterizations of such curves are given by means of their curvatures and torsions. Also some special curves which have Mannheim curves and Mannheim partner curves are investigated. In the fourth chapter , Generalized Mannheim curves and Mannheim partner curves according to Frenet frame in 4-dimensional Euclidean space are defined and the characterizations of such curves are given by means of their curvature functions.