The geometry of totally geodesic Riemannian foliations
Let \(\mathcal F\) be a totally geodesic, Riemannian foliation of a complete Riemannian manifold \(M\). Let \(H\) be the orthogonal complement to the distribution \(T{\mathcal F}\). The author defines a metric connection \(\tilde \nabla\) on \(M\) for which both \(T{\mathcal F}\) and \(H\) are parallel. The distribution \(H\) is integrable if and only if \(\tilde \nabla\) is torsion--free.
scientific article; zbMATH DE number 1541525