On C-Parallel Legendre Curves in Non-Sasakian Contact Metric Manifolds

Abstract

We consider Legendre curves in $(2n+1)$-dimensional non-Sasakian contact metric manifolds whose mean curvature vector fields are $\mathcal{C}$-parallel or $\mathcal{C}$-proper in tangent or normal bundle. We obtain the curvature characterizations of these curves. Moreover, we give some examples of these kinds of curves which satisfy the conditions of our results.