On the Frenet planes

This thesis consists of five chapters. In the first chapter "Introduction" part has been presented. In the second chapter, some basic definitions and concepts in Euclidean and Minkowski 3-spaces have been presented. In the third chapter, some cases that Frenet planes of a given space curve in Euclidean 3-space 𝔼3 are Frenet planes of another space curve have been investigated. In the fourth chapter, the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space 𝔼13 also is any spacelike Frenet plane of another space curve in the same space has been investigated. In the fifth chapter, the possibility of whether any timelike Frenet plane of a given space curve in Minkowski 3-space 𝔼13 also is any timelike Frenet plane of another space curve in the same space has been investigated. Key words: Frenet planes; curves; Mannheim curve; Salkowski and Anti-Salkowski curves; spacelike and timelike plane.