Anti-torqued and torqued curves in Riemannian manifolds

In this paper, we introduce the notions of anti-torqued and torqued curves $\gamma$ in a Riemannian manifold $(\widetilde{M},\langle,\rangle)$, defined as curves for which $\langle N^\gamma,V\rangle$ is constant, where $N^\gamma$ is the unit principal normal vector field of $\gamma$ and $V$ is a globally defined anti-torqued or torqued vector field on $\widetilde{M}$. We characterize and classify these curves through systems of differential equations involving their invariants. Several examples are also provided.