Dual Thurston norm of Euler classes of foliations on negative curvature 3-Manifolds

In this paper we give an upper bound estimate on the dual Thurston norm of the Euler class of an arbitrary smooth foliation F of dimension one defined on a closed three-dimensional orientable manifold M³ of negative curvature, which depends on the constants bounded the injectivity radius inj(M³), the volume Vol(M³), sectional curvature of the manifold M³ and the mean curvature modulus of the leaves of the foliation F.