  In this paper we study several dynamical properties of the riemannian
$1$-dimensional foliation $\mathcal{L}$ on an oriented closed 3-manifold $M$.
Carriere classified such pairs $(M,\mathcal{L})$. Using the classification we
prove the nonhyperbolicity of $(M,\mathcal{L})$. Also we describe in detail
recurrence points, $\omega$-limit sets and attractors.
