De Rham decomposition theorems for foliated manifolds

Robert A. Blumenthal; James J. Hebda

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 2, page 183-198
  • ISSN: 0373-0956

Abstract

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We prove that if M is a complete simply connected Riemannian manifold and F is a totally geodesic foliation of M with integrable normal bundle, then M is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.

How to cite

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Blumenthal, Robert A., and Hebda, James J.. "De Rham decomposition theorems for foliated manifolds." Annales de l'institut Fourier 33.2 (1983): 183-198. <http://eudml.org/doc/74583>.

@article{Blumenthal1983,
abstract = {We prove that if $M$ is a complete simply connected Riemannian manifold and $F$ is a totally geodesic foliation of $M$ with integrable normal bundle, then $M$ is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.},
author = {Blumenthal, Robert A., Hebda, James J.},
journal = {Annales de l'institut Fourier},
keywords = {totally geodesic foliation with integrable normal bundle; product foliations; decomposition theorem for Riemannian foliations},
language = {eng},
number = {2},
pages = {183-198},
publisher = {Association des Annales de l'Institut Fourier},
title = {De Rham decomposition theorems for foliated manifolds},
url = {http://eudml.org/doc/74583},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Blumenthal, Robert A.
AU - Hebda, James J.
TI - De Rham decomposition theorems for foliated manifolds
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 2
SP - 183
EP - 198
AB - We prove that if $M$ is a complete simply connected Riemannian manifold and $F$ is a totally geodesic foliation of $M$ with integrable normal bundle, then $M$ is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.
LA - eng
KW - totally geodesic foliation with integrable normal bundle; product foliations; decomposition theorem for Riemannian foliations
UR - http://eudml.org/doc/74583
ER -

References

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  3. [3] R. A. BLUMENTHAL, Riemannian foliations with parallel curvature, Nagoya Math. J. (to appear). Zbl0508.57020
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