Relèvement d’un drapeau riemannien et drapeaux de Lie du tore hyperbolique n + 1 -dimensionnel

Hassimiou Diallo[1]

  • [1] Ecole Normale Supérieure Laboratoire de Mathématiques Département des Sciences et Technologie 08 BP 10 Abidjan CÔTE D’IVOIRE

Annales mathématiques Blaise Pascal (2005)

  • Volume: 12, Issue: 2, page 245-258
  • ISSN: 1259-1734

Abstract

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A flag on a manifold M is an increasing sequence of foliations ℱ 1 , ⋯ , ℱ p on this manifold, where for each i , dim ℱ i = i . The aim of this paper is to etablish that any flag of riemannian foliations 𝒟 = ℱ 1 , ⋯ , ℱ p on a compact and connected manifold, lifts on the bundle of transverse direct orthonormal frames of ℱ p to a flag of transversally parallelizable foliations. This result permits us to obtain a classification of riemannian flags of a n + 1 -dimensional compact manifold for which the dimension of the structural Lie algebra of the flow is equal to n or n - 1 .

How to cite

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Diallo, Hassimiou. "Relèvement d’un drapeau riemannien et drapeaux de Lie du tore hyperbolique $n+1$-dimensionnel." Annales mathématiques Blaise Pascal 12.2 (2005): 245-258. <http://eudml.org/doc/10519>.

@article{Diallo2005,
affiliation = {Ecole Normale Supérieure Laboratoire de Mathématiques Département des Sciences et Technologie 08 BP 10 Abidjan CÔTE D’IVOIRE},
author = {Diallo, Hassimiou},
journal = {Annales mathématiques Blaise Pascal},
keywords = {feuilletages; feuilletages riemanniens; drapeaux riemanniens; drapeaux de Lie; foliation; flag; Riemannian flag; -dimensional hyperbolic torus},
language = {fre},
month = {7},
number = {2},
pages = {245-258},
publisher = {Annales mathématiques Blaise Pascal},
title = {Relèvement d’un drapeau riemannien et drapeaux de Lie du tore hyperbolique $n+1$-dimensionnel},
url = {http://eudml.org/doc/10519},
volume = {12},
year = {2005},
}

TY - JOUR
AU - Diallo, Hassimiou
TI - Relèvement d’un drapeau riemannien et drapeaux de Lie du tore hyperbolique $n+1$-dimensionnel
JO - Annales mathématiques Blaise Pascal
DA - 2005/7//
PB - Annales mathématiques Blaise Pascal
VL - 12
IS - 2
SP - 245
EP - 258
LA - fre
KW - feuilletages; feuilletages riemanniens; drapeaux riemanniens; drapeaux de Lie; foliation; flag; Riemannian flag; -dimensional hyperbolic torus
UR - http://eudml.org/doc/10519
ER -

References

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  1. A. El Kacimi Alaoui, M. Nicolau, A class of C ∞ stable foliations, Ergod. Th. and Dynam. Sys. 13 (1993), 667-704 Zbl0801.58038MR1257030
  2. R. Almeida, P. Molino, Flots Riemanniens sur les 4-variétés compactes, Tôhoku Mathematical Journal 38 (1986), 313-326 Zbl0603.57017MR843815
  3. B Bossoto, H Diallo, Sur les drapeaux de feuilletages riemanniens, JP Journal of Geometry and Topology, University of Allahabad, INDIA 2 (2002), 281-288 MR2110299
  4. H. Diallo, Sur les drapeaux de Lie, Afrika Mathematika 13 (2002), 75-86 Zbl1044.57010MR1924534
  5. E. Fédida, Feuilletages du plan. Feuilletages de Lie, (1973) Zbl0267.57019
  6. P. Molino, Géométrie globale des feuilletages riemanniens, Proc. Kon. Nederland Akad Ser. A 85 (1982), 45-76 Zbl0516.57016MR653455
  7. Y Carrière, Flots riemanniens, Structures transverses des feuilletages, 116 (1984), 31-52 Zbl0548.58033MR755161

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