In this paper we give an upper bound estimate on the dual Thurston norm of the Euler class of an arbitrary smooth foliation $\mathcal{ F}$ of dimension one defined on a closed three-dimensional orientable manifold $M^3$ of negative curvature, which depends on the constants bounded the injectivity radius $inj(M^3)$, the volume $Vol(M^3)$, sectional curvature of the manifold $M^3$ and the mean curvature modulus of the leaves of the foliation $\mathcal{ F}$.
Categories: math.GT math.DG