The curve congruences in 3- euclidean space

The "mode" relation used in modular arithmetic can be applied by using the linear algebra substructure to Frenet vectors in curve theory and new curve pairs can be defined by using Frenet vectors and Frenet planes. This thesis consists of five chapters. In the first chapter, the concepts of linear algebra and differential geometry, which will form the basis of the thesis, are given. In the second part, planar curves and congruent curves defined with Frenet vectors are examined. In the third chapter, congruent curves of curves defined in 3-dimensional space according to Frenet vectors are investigated. In the fourth chapter, the congruent curves of the spherical indicator curves of the space curves according to the vectors of the curve were investigated. In the fifth chapter, congruent curves of space curves and spherical indicator curves according to Frenet planes, which can be the continuation of this thesis, are introduced. Keywords : Congruent curves, curve pairs, shperical indicatrix.