Özet:
The aim of this thesis is to investigate Smarandache curves of the directional curves in
Euclidean and Minkowski 3-space using the q-frame. Even though q-frame is defined by a
projection vector, quasi normal and quasi binormal vectors.
This study consists of five chapters. In the introduction and literature research sections,
some information about the history and development of the subject are given. In the third
chapter, some definitions and theorems which will be used throughout this thesis are mentioned
and q-frame is emphasized. In addition to the relations between the Frenet frame and q-frame,
curvatures of the spacelike and timelike curves due to the k projection vector in Minkowski
3-space are given. In the fourth chapter, Smarandache curves with q-frame in Euclidean space
are defined and some equations related to Smarandache curves are discussed. For each curve
we defined q-frame vectors and q-curvatures were obtained. In the fifth chapter, definitions and
theorems about timelike Bertrand, Mannheim and involute-evolute curve pairs in Minkowski
3-space are given. In these curves, q-frame vectors and q-curvatures were obtained
