Some de Rham cohomology groups associated to a subfoliation

Abstract

In this paper, we consider a (q₁, q₂)-codimensional subfoliation (F₁, F₂) on a Riemannian manifold M. We give a decomposition of the exterior derivative with respect to this subfoliation. We identify two new de Rham cohomology groups associated with (F₁, F₂). These groups are topological invariants of manifold (M, F₁, F₂).