Geometry of curve pairs

Abstract: This study, prepared as a master's thesis, consists of four chapters. In the first chapter, which serves as the introduction, fundamental information on curve couples is presented, and previous studies conducted in this field are reviewed. In the second chapter, in order to ensure the comprehensibility of the thesis, differentiable functions, planar curves, and curves in R^3 and R^4 are discussed. In addition, roof curves in R^3 and R^4 are analyzed. The third chapter is devoted to the investigation of the relationships associated with Involute–Evolute curve couples, Bertrand curve couples, and Mannheim curve couples. Moreover, the properties of Bertrand and Mannheim curve couples in roof curves are examined. In the fourth and final chapter, Bertrand and Mannheim curve couples in the four-dimensional Euclidean space R^4 are considered. Furthermore, the relationships between Bertrand and Mannheim curve couples in roof curves are presented.