# Transversely homogeneous foliations

Annales de l'institut Fourier (1979)

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

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topBlumenthal, 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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- [9] M. SPIVAK, A comprehensive introduction to differential geometry, vol. I, Publish or Perish, Boston, 1970. Zbl0202.52001
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