FINITENESS AND TENSENESS THEOREMS FOR RIEMANNIAN FOLIATIONS

We prove a finiteness theorem for the spectral sequence (E-i(del),(d(d el))(i)) associated to a Riemannian foliation F on a compact manifold M, and to a flat vector bundle E over M with hat connection del. Using this result we prove that every Riemannian foliation on a compact man ifold is tense (in the sense of [F. W. Kamber and Ph. Tondeur, Foliati ons and metrics, Progr. Math., vol. 32, 1983, pp. 103-152]). We also s how that the main tautness theorems for Riemannian foliations on compa ct manifolds, which were proved by several authors, are immediate cons equences of our results.