Some special curves in contact manifolds

In the first part of this three-part study, some basic concepts are given to better understand the subject. In the second chapter, the basic properties of Riemann manifold, Contact manifold, Contact Lorentzain manifold and Sasakian manifolds are mentioned. In the last section, Frenet elements were calculated by examining Frenet curves on δ-Lorentzian trans-Sasakian manifolds. Then, the necessary conditions for these curves to remain in some subspaces are given. Afterwards, Frenet elements were calculated by giving the Frenet curve of the curves on 3-dimensional normal almost contact manifolds. After this calculation, the necessary conditions for these curves to remain in some subspaces are given. Finally, Frenet equations and elements of some curves on a 3-dimensional normal almost contact pseudo-metric manifolds were calculated. Necessary conditions for these curves to remain in some subspaces are given. Keywords: Contact manifold; Sasakian manifold; Frenet curve.