ABSTRACT
The theorems proved about such structures tend to be either topological obstructions on the characteristic algebra or classifications of all manifolds admitting such foliations. One criterion of naturality would seem to be a sort of stability; a geometric structure on a foliation is stable if all nearby foliations also possess that structure. The condition that a foliation be Riemannian for some metric is very easily seen to be an instable notion. The only foliations of the 2-dimensional torus T that are Riemannian are conjugate to foliations by either skew lines or circles; but a generic deformation of such a foliation has limit cycles, and so Riemannian. The nongeodesible flow is a deformation of the Hopf foliation to one with only two closed linked closed orbits, one repelling and the other attracting. A theorem of Sullivan is then used to show that this foliation is geodesible.
