Tenseness of Riemannian flows
Annales de l'Institut Fourier, Volume 64 (2014) no. 4, pp. 1419-1439.

We show that any transversally complete Riemannian foliation of dimension one on any possibly non-compact manifold M is tense; namely, M 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 well known results including Masa’s characterization of tautness.

On montre que tout feuilletage riemannien de dimension un transversalement complet sur une variété M, éventuellement non compacte, est étiré ; c’est à dire, il existe une métrique riemanniene sur M pour laquelle la forme de courbure moyenne de est basique. Ceci est une généralisation partielle d’un résultat de Domínguez, qui dit que tout feuilletage riemannien sur une variété compacte est étiré. La preuve s’appuie sur certains résultats de Molino et Sergiescu, et elle est plus simple que la première démonstration de Domínguez. Comme application, on généralise certains résultats bien connus, comme la caractérisation des feuilletages tendus par Masa.

DOI: 10.5802/aif.2885
Classification: 53C12,  57R30,  37C10
Keywords: Riemannian foliation, taut foliation, mean curvature, basic cohomology
Nozawa, Hiraku 1; Royo Prieto, José Ignacio 2

1 Department of Mathematical Sciences College of Science and Engineering Ritsumeikan University 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577 (Japan)
2 Universidad del País Vasco UPV/EHU Departamento de Matemática Aplicada Alameda de Urquijo s/n 48013 Bilbao (Spain)
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Nozawa, Hiraku; Royo Prieto, José Ignacio. Tenseness of Riemannian flows. Annales de l'Institut Fourier, Volume 64 (2014) no. 4, pp. 1419-1439. doi : 10.5802/aif.2885. http://www.numdam.org/articles/10.5802/aif.2885/

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