Abstract: | A smooth fibration of 3 by oriented lines is given by a smoothunit vector field V on 3 all of whose integral curves are straightlines. Such a fibration is said to be nondegenerate if dV vanishesonly in the direction of V. Let be the space of oriented linesof 3 endowed with its canonical pseudo-Riemannian neutral metric.We characterize the nondegenerate smooth fibrations of 3 byoriented lines as the closed (in the relative topology) definiteconnected surfaces in . In particular, local conditions on imply the existence of a global fibration. Besides, for anysuch fibration the base space is diffeomorphic to the open discand the directions of the fibers form an open convex set ofthe two-sphere. We characterize as well, in a similar way, thesmooth (possibly degenerate) fibrations. |