A curve theory on sliced almost contact manifolds

We have realized a gap between almost contact metric manifolds and contact metric manifolds in our studies. The examples that were given as Sasaki manifolds don't satisfy the condition of being contact metric manifold. As a result of our work, the sliced almost contact manifolds were formed and defined in \cite{MG}. In this paper we applied the theory of sliced almost contact manifolds to curves as a curve theory in three dimensional space. We define the $\pi-regular$ and $\pi-Legendre$ curves, also we give basic theorems on $\pi-Legendre$ curves and an example to $\pi-Legendre$ curves.