Tenseness of Riemannian flows
We show that any transversally complete Riemannian foliation of dimension one on any possibly non-compact manifold is tense; namely, admits a Riemannian metric such that the mean curvature form of is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize some...