ON THE CURVATURE GROUPS OF A RIEMANNIAN FOLIATION

Abstract

We study basic curvature groups H • B (M, F ,� ) associated to a foliated Riemannian manifold (M, F ,g )[generalizingVaisman’s curvature groups of a Riemannian space form; cf. (The curvature groups of a space form, Ann. Sc. Norm. Super. Pisa 22 (1968), 331–341.)] and their relationship to the basic cohomology groups of (M, F ). We show that H • B (M, F ,� ) = 0 for any Einstein foliation F of non-zero transverse scalar curvature.