A characterization of Riemannian flows

Tondeur, Philippe

doi:10.1090/S0002-9939-97-04036-7

A characterization of Riemannian flows
HTML articles powered by AMS MathViewer

by Philippe Tondeur PDF

Proc. Amer. Math. Soc. 125 (1997), 3403-3405 Request permission

Abstract:

We prove that a flow on a closed manifold is Riemannian if and only if it is locally generated by Killing vector fields for a Riemannian metric.

References

Yves Carrière, Flots riemanniens, Astérisque 116 (1984), 31–52 (French). Transversal structure of foliations (Toulouse, 1982). MR 755161
Demetrio Domínguez, A tenseness theorem for Riemannian foliations, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 11, 1331–1335 (English, with English and French summaries). MR 1338282, DOI 10.1353/ajm.1998.0048
James J. Hebda, Curvature and focal points in Riemannian foliations, Indiana Univ. Math. J. 35 (1986), no. 2, 321–331. MR 833397, DOI 10.1512/iumj.1986.35.35019
Franz W. Kamber and Philippe Tondeur, Foliations and metrics, Differential geometry (College Park, Md., 1981/1982) Progr. Math., vol. 32, Birkhäuser Boston, Boston, MA, 1983, pp. 103–152. MR 702530
Hong Kyung Pak, On one-dimensional metric foliations in Einstein spaces, Illinois J. Math. 36 (1992), no. 4, 594–599. MR 1215797
Maung Min-Oo, Ernst A. Ruh, and Philippe Tondeur, Vanishing theorems for the basic cohomology of Riemannian foliations, J. Reine Angew. Math. 415 (1991), 167–174. MR 1096904
Pierre Molino and Vlad Sergiescu, Deux remarques sur les flots riemanniens, Manuscripta Math. 51 (1985), no. 1-3, 145–161 (French, with English summary). MR 788676, DOI 10.1007/BF01168350
Bruce L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119–132. MR 107279, DOI 10.2307/1970097
Philippe Tondeur, Foliations on Riemannian manifolds, Universitext, Springer-Verlag, New York, 1988. MR 934020, DOI 10.1007/978-1-4613-8780-0