Tzitzeica smarandache curves in three dimensional euclidean space

The aim of this study is to examine the relations between Tzitzeica curves and Smarandache curves in Euclidean space. In addition, the necessary and sufficient conditions for Smarandache curves to be Tzitzeica curves in 3-dimensional Euclidean space are investigated and relevant examples are given. During the thesis process, some existing definitions were used and new results were obtained by making additions. This thesis consists of four parts. The first part is the introduction. In this section, the studies carried out to date are mentioned. In the second part, the basic concepts and definitions used and needed throughout the study are included. In the third part, TN1, TN2, N1N2, TN1N2 Smarandache curves are discussed and the conditions for these curves to become Tzitzeica curves (Tz-curve) are examined one by one and the resulting theorems and results are expressed in detail. In the fourth part, TN1, TN2, N1N2, TN1N2 Smarandache curves of some unit speed curves discussed are found and presented with proofs whether these curves are Tzitzeica curves (Tz-curve).