On Lie algebras of vector fields related to Riemannian foliations

Tomasz Rybicki

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 2, page 111-122
  • ISSN: 0066-2216

Abstract

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Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.

How to cite

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Tomasz Rybicki. "On Lie algebras of vector fields related to Riemannian foliations." Annales Polonici Mathematici 58.2 (1993): 111-122. <http://eudml.org/doc/262263>.

@article{TomaszRybicki1993,
abstract = {Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.},
author = {Tomasz Rybicki},
journal = {Annales Polonici Mathematici},
keywords = {Riemannian foliation; Lie algebra; ideal; isomorphism; vector field; generalized manifold; stratification; space of leaves; singular foliation; Riemannian foliations of compact, connected manifolds; Lie algebra of vector fields; Lie algebra of foliated vector fields; Lie algebra isomorphism; Satake diffeomorphism},
language = {eng},
number = {2},
pages = {111-122},
title = {On Lie algebras of vector fields related to Riemannian foliations},
url = {http://eudml.org/doc/262263},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Tomasz Rybicki
TI - On Lie algebras of vector fields related to Riemannian foliations
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 2
SP - 111
EP - 122
AB - Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
LA - eng
KW - Riemannian foliation; Lie algebra; ideal; isomorphism; vector field; generalized manifold; stratification; space of leaves; singular foliation; Riemannian foliations of compact, connected manifolds; Lie algebra of vector fields; Lie algebra of foliated vector fields; Lie algebra isomorphism; Satake diffeomorphism
UR - http://eudml.org/doc/262263
ER -

References

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  10. [10] M. Pierrot, Orbites des champs feuilletés pour un feuilletage riemannien sur une variété compacte, C. R. Acad. Sci. Paris 301 (1985), 443-445. Zbl0593.58003
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  12. [12] T. Rybicki, On the Lie algebra of a transversally complete foliation, Publ. Sec. Mat. Univ. Autònoma Barcelona 31 (1987), 5-16. Zbl0637.57018
  13. [13] T. Rybicki, Lie algebras of vector fields and codimension one foliations, Publ. Mat. 34 (1990), 311-321. Zbl0721.57016
  14. [14] G. W. Schwarz, Lifting smooth homotopies of orbit spaces, Publ. IHES 51 (1980), 37-135. Zbl0449.57009
  15. [15] R. A. Wolak, Maximal subalgebras in the algebra of foliated vector fields of a Riemannian foliation, Comment. Math. Helv. 64 (1989), 536-541. Zbl0695.53023

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