Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A characterization of Riemannian flows

Author: Philippe Tondeur
Journal: Proc. Amer. Math. Soc. 125 (1997), 3403-3405
MSC (1991): Primary 53C12, 57R30
MathSciNet review: 1415373
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Y. Carrière, Flots Riemanniens, Structure transverse des feuilletages, Astérisque 116 (1984), 31-52. MR 86m:58125a
  • 2. D. Domínguez, A tenseness theorem for Riemannian foliations, C. R. Acad. Sci. Paris 320 (1995), 1331-1335. MR 96d:53025
  • 3. J. Hebda, Curvature and focal points in Riemannian foliations, Indiana Univ. Math. J. 35 (1986), 321-331. MR 87g:53051
  • 4. F. Kamber and Ph. Tondeur, Foliations and metrics, Progress in Math. 32 (1983), 103-152. MR 85a:57017
  • 5. H. Kyung Pak, On one-dimensional metric foliations in Einstein spaces, Ill. J. Math. 36 (1992), 594-599. MR 94d:53046
  • 6. M. Min-Oo, E. Ruh and Ph. Tondeur, Vanishing theorems for the basic cohomology of Riemannian foliations, J. Reine Angew. Math. 415 (1991), 167-174. MR 92b:58218
  • 7. P. Molino and V. Sergiescu, Deux remarques sur les flots riemanniens, Manuscripta Math. 51 (1985), 145-161. MR 86h:53035
  • 8. B. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), 119-132. MR 21:6004
  • 9. Ph. Tondeur, Foliations on Riemannian manifolds, Universitext, Springer-Verlag, New York, 1988. MR 89e:53052

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C12, 57R30

Retrieve articles in all journals with MSC (1991): 53C12, 57R30

Additional Information

Philippe Tondeur
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 West Green Street, Urbana, Illinois 61801

Received by editor(s): June 19, 1996
Communicated by: Christopher Croke
Article copyright: © Copyright 1997 American Mathematical Society