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Book Review

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Book Information:

Author: Philippe Tondeur
Title: Foliations on Riemannian manifolds
Additional book information: Universitext, Springer-Verlag, Berlin, Heidelberg, London, New York, Paris, Tokyo, 1988, 247 pp. $29.80. ISBN 0-387-96707-9 and ISBN 3-540-96707-9.

Author: Pierre Molino
Title: Riemannian foliations
Additional book information: (Translated by Grant Cairns). Progress in Mathematics, vol. 73, Birkhäuser, Boston, Basel, 1986, 339 pp. $44.00. ISBN 0-8176-3370-7 and ISBN 3-7643-3370-7.

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

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  • Aziz El Kacimi-Alaoui and Gilbert Hector, Décomposition de Hodge sur l’espace des feuilles d’un feuilletage riemannien, C. R. Acad. Sci. Paris Sér. I Math. 298 (1984), no. 13, 289–292 (French, with English summary). MR 765425
  • A. El Kacimi-Alaoui and G. Hector, Décomposition de Hodge basique pour un feuilletage riemannien, Ann. Inst. Fourier (Grenoble) 36 (1986), no. 3, 207–227 (French, with English summary). MR 865667
  • Aziz El Kacimi-Alaoui, Vlad Sergiescu, and Gilbert Hector, La cohomologie basique d’un feuilletage riemannien est de dimension finie, Math. Z. 188 (1985), no. 4, 593–599 (French). MR 774559, https://doi.org/10.1007/BF01161658
  • Franz W. Kamber and Philippe Tondeur, Duality for Riemannian foliations, Singularities, Part 1 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 609–618. MR 713097
  • 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
  • Franz W. Kamber and Philippe Tondeur, Duality theorems for foliations, Astérisque 116 (1984), 108–116. Transversal structure of foliations (Toulouse, 1982). MR 755165
  • Franz W. Kamber and Philippe Tondeur, de Rham-Hodge theory for Riemannian foliations, Math. Ann. 277 (1987), no. 3, 415–431. MR 891583, https://doi.org/10.1007/BF01458323
  • [M1] P. Molino, Sur la géométrie transverse des feuilletages, Ann. Inst. Fourier (Grenoble) 25 (1975), 279-284. MR 391123
  • [M2] P. Molino, Etude des feuilletages transversalement complets et applications, Ann. Sci. École Norm. Sup. 10 (1977), 289-307. MR 458446
  • Pierre Molino, Feuilletages riemanniens sur les variétés compactes; champs de Killing transverses, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), no. 7, A421–A423 (French, with English summary). MR 554633
  • Pierre Molino, Géométrie globale des feuilletages riemanniens, Nederl. Akad. Wetensch. Indag. Math. 44 (1982), no. 1, 45–76 (French). MR 653455
  • [Rb] G. Reeb, Sur certains propriétés topologiques des variétés feuilletées, Hermann, Paris, 1952. MR 55692
  • [Rt1] B. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), 119-132. MR 107279
  • [Rt2] B. Reinhart, Harmonic integrals on foliated manifolds, Amer. J. Math. 81 (1959), 529-536. MR 107280

Review Information:

Reviewer: L. Conlon
Journal: Bull. Amer. Math. Soc. 23 (1990), 583-588
DOI: https://doi.org/10.1090/S0273-0979-1990-15990-7
American Mathematical Society