Negative exterior curvature foliations on compact Riemannian manifolds (Q1277574)

A foliation on a Riemannian manifold is called hyperbolic if the two-dimensional sectional curvature of its leaves is less than the two-dimensional sectional curvature of the ambient space along elements tangent to the leaves. If the dimension of the leaves is \(l\), then the minimal dimension of an ambient space admitting a hyperbolic foliation equals \(2l-1\). The following theorem is proved in the paper. Theorem. Suppose that a simply connected compact Riemannian manifold \(M^{2l-1}\) admits a hyperbolic foliation \(F^l\). If \(l=2,3,4\), then the manifold \(M^{2l-1}\) is parallelizable.