Almost contact curves

This study which is designed as master science thesis covers three chapters. In the fi rst chapter we give some basic concepts about curves, Riemannian manifolds, contact manifolds, K-Contact manifolds, Sasakian manifolds, Lorentzian contact manifolds, almost paracontact metric manifolds and normal almost paracontact metric manifolds for the rest of the thesis that readers can easily understand. In the second chapter, fi rstly, Legendre curves and some examples are given. Furthermore, in this chapter, we investigate slant curves, slant curves in 3-dimensional normal almost geometry and Legendre curves in Lorentzian Sasaki spaces. In the third chapter, slant curves in 3-dimensional normal almost paracontact metric manifolds, null slant curves, null normal slant curves, Legendre curves in 3-dimensional normal almost paracontact metric manifolds and Legendre curves on 3-dimensional Heisenberg groups are given.