Transversely homogeneous foliations

Robert A. Blumenthal

Annales de l'institut Fourier (1979)

  • Volume: 29, Issue: 4, page 143-158
  • ISSN: 0373-0956

Abstract

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A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space G / K which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when K is compact. We investigate the relationship between the structure equations of G and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special case, we study the transversely elliptic, Euclidean, and hyperbolic foliations.

How to cite

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Blumenthal, Robert A.. "Transversely homogeneous foliations." Annales de l'institut Fourier 29.4 (1979): 143-158. <http://eudml.org/doc/74428>.

@article{Blumenthal1979,
abstract = {A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space $G/K$ which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when $K$ is compact. We investigate the relationship between the structure equations of $G$ and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special case, we study the transversely elliptic, Euclidean, and hyperbolic foliations.},
author = {Blumenthal, Robert A.},
journal = {Annales de l'institut Fourier},
keywords = {Transversely Homogeneous Foliations; Structure Equations; Normal Bundle of the Foliation; Differential Forms Characterization; Transversely Elliptic; Transversely Euclidean; Transversely Hyperbolic},
language = {eng},
number = {4},
pages = {143-158},
publisher = {Association des Annales de l'Institut Fourier},
title = {Transversely homogeneous foliations},
url = {http://eudml.org/doc/74428},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Blumenthal, Robert A.
TI - Transversely homogeneous foliations
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 4
SP - 143
EP - 158
AB - A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space $G/K$ which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when $K$ is compact. We investigate the relationship between the structure equations of $G$ and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special case, we study the transversely elliptic, Euclidean, and hyperbolic foliations.
LA - eng
KW - Transversely Homogeneous Foliations; Structure Equations; Normal Bundle of the Foliation; Differential Forms Characterization; Transversely Elliptic; Transversely Euclidean; Transversely Hyperbolic
UR - http://eudml.org/doc/74428
ER -

References

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  5. [5] R. PALAIS, A global formulation of the Lie theory of transformation groups, Memoirs of the Amer. Math. Soc., 22 (1957). Zbl0178.26502MR22 #12162
  6. [6] J. F. PLANTE, Foliations with measure preserving holonomy, Ann. of Math., 102 (1975), 327-361. Zbl0314.57018MR52 #11947
  7. [7] M. S. RAGHUNATHAN, Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (68), Springer-Verlag, Berlin, 1972. Zbl0254.22005MR58 #22394a
  8. [8] B. REINHART, Foliated manifolds with bundle-like metrics, Ann. of Math., (1), 69 (1959), 119-132. Zbl0122.16604MR21 #6004
  9. [9] M. SPIVAK, A comprehensive introduction to differential geometry, vol. I, Publish or Perish, Boston, 1970. Zbl0202.52001
  10. [10] J. TITS, Free subgroups in linear groups, J. of Alg., 20 (1972), 250-270. Zbl0236.20032MR44 #4105
  11. [11] J. WOLF, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. of Diff. Geom., 2 (1968), 421-446. Zbl0207.51803MR40 #1939

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