Dynamics of riemannian 1-foliations on $3$-manifolds

Abstract

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.