Riemannian foliations with parallel or harmonic basic forms

Fida El Chami; Georges Habib; Roger Nakad

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 1, page 51-65
  • ISSN: 0044-8753

Abstract

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In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.

How to cite

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El Chami, Fida, Habib, Georges, and Nakad, Roger. "Riemannian foliations with parallel or harmonic basic forms." Archivum Mathematicum 051.1 (2015): 51-65. <http://eudml.org/doc/270057>.

@article{ElChami2015,
abstract = {In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.},
author = {El Chami, Fida, Habib, Georges, Nakad, Roger},
journal = {Archivum Mathematicum},
keywords = {Riemannian foliation; parallel and harmonic basic forms; O’Neill tensor; Riemannian foliation; parallel and harmonic basic forms; O'Neill tensor},
language = {eng},
number = {1},
pages = {51-65},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Riemannian foliations with parallel or harmonic basic forms},
url = {http://eudml.org/doc/270057},
volume = {051},
year = {2015},
}

TY - JOUR
AU - El Chami, Fida
AU - Habib, Georges
AU - Nakad, Roger
TI - Riemannian foliations with parallel or harmonic basic forms
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 1
SP - 51
EP - 65
AB - In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.
LA - eng
KW - Riemannian foliation; parallel and harmonic basic forms; O’Neill tensor; Riemannian foliation; parallel and harmonic basic forms; O'Neill tensor
UR - http://eudml.org/doc/270057
ER -

References

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  7. O’Neill, B., 10.1307/mmj/1028999604, Michigan Math. J. 13 (1966), 459–469. (1966) MR0200865DOI10.1307/mmj/1028999604
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