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Sufficient conditions for a bundle-like foliation to admit a Riemannian submersion onto its leaf space


Author: Richard H. Escobales
Journal: Proc. Amer. Math. Soc. 84 (1982), 280-284
MSC: Primary 53C12; Secondary 57R30
DOI: https://doi.org/10.1090/S0002-9939-1982-0637184-5
MathSciNet review: 637184
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Abstract: This note furnishes a necessary and sufficient condition for a bundlelike foliation to be defined globally by a Riemannian submersion.


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

  • [1] R. Blumenthal, Riemannian homogeneous foliations without holonomy (preprint). MR 632653 (82m:57013)
  • [2] C. Ehresmann, Les connexions infinitesmals, Colloq. Topologie (Espaces Fibres), Bruxelles, 1950, pp. 29-95.
  • [3] Richard H. Escobales, Jr., The integrability tensor for bundle-like foliations, Trans. Amer. Math. Soc. (to appear). MR 642345 (84b:57017)
  • [4] A. Haefliger, Variétés feuilletées, Ann. Scuola Norm Sup. Pisa (3) 16 (1962), 367-379. MR 0189060 (32:6487)
  • [5] R. Hermann, A sufficient condition that a map of Riemannian manifolds be a fiber bundle, Proc. Amer. Math. Soc. 11 (1960), 236-242. MR 0112151 (22:3006)
  • [6] -, On the differential geometry of foliations, Ann. of Math. (2) 72 (1960), 445-457. MR 0142130 (25:5523)
  • [7] H. Blaine Lawson, Jr., Foliations, Bull. Amer. Math. Soc. 80 (1974), 369-418. MR 0343289 (49:8031)
  • [8] -, The quantitative theory of foliations, CBMS Reg. Conf. Ser. in Math., vol. 27, Amer. Math. Soc. Providence, R. I., 1977. MR 0448368 (56:6675)
  • [9] T. Nagano, On fibred Riemann manifolds, Sci. Papers College Gen. Ed. Univ. Tokyo 10 (1960), 17-27. MR 0157325 (28:560)
  • [10] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. MR 0200865 (34:751)
  • [11] R. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc. No. 22 (1957). MR 0121424 (22:12162)
  • [12] B. L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119-131. MR 0107279 (21:6004)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0637184-5
Article copyright: © Copyright 1982 American Mathematical Society

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