Tenseness of Riemannian flows
arXiv:1206.4965
Abstract
We show that any transversally complete Riemannian foliation F of dimension one on any possibly non-compact manifold M is tense; namely, (M,F) admits a Riemannian metric such that the mean curvature form of F is basic. This is a partial generalization of a result of Dominguez, 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 Dominguez. As an application, we generalize some well known results including Masa's characterization of tautness.
14 pages. Accepted for publication in Annales de l'Institut Fourier. We have performed some changes in this final version, following the suggestions of the referee. Among other changes, several typos and the proof of Theorem 1.4 have been corrected