Structure of a leaf of some codimension one riemannian foliation
Some properties of the range on an open leaf of some codimension-one foliation are shown. They are different from the known properties of the distance of leaves. They imply that leaf is of fibred type over a complete Riemannian manifold with boundary, as well that there exists some vector field on . If is parallel then is diffeomorphic to and has non-positive curvature.