FURTHER GEOMETRY OF THE MEAN-CURVATURE ONE-FORM AND THE NORMAL PLANE FIELD ONE-FORM ON A FOLIATED RIEMANNIAN MANIFOLD

For foliations on Riemannian manifolds, we develop elementary geometri c and topological properties of the mean curvature one-form kappa and the normal plane field one-form beta. Through examples, we show that a n important result of Kamber-Tondeur on kappa is in general a best pos sible result. But we demonstrate that their bundle-like hypothesis can be relaxed somewhat in codimension 2. We study the structure of umbil ic foliations in this more general context and in our final section es tablish some analogous results for flows.