Let (𝓜,g) be a Riemannian manifold and let
1,
2,
3 be mutually orthogonal distributions on 𝓜 of dimensions p1, p2,P3 such that p1 + p2 + p3 = dim 𝓜. We assume that , and
1, ⊕
2 are integrable and that all the geodesies of 𝓜 with initial tangent vector in
2 remain tangent to
2. Then, we prove that Pontk(
2, ⊕
3) = 0 for k > p2 + 2p3, where Pontk(
2, ⊕
3) is the subspace of the Pontrjagin algebra of
2 ⊕
3 generated by forms of degree k.