Parallelisability conditions for differentiable three-webs

Alena Vanžurová

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 1, page 75-84
  • ISSN: 0044-8753

Abstract

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Our aim is to find conditions under which a 3-web on a smooth 2 n -dimensional manifold is locally equivalent with a web formed by three systems of parallel n -planes in R 2 n . We will present here a new approach to this “classical” problem using projectors onto the distributions of tangent subspaces to the leaves of foliations forming the web.

How to cite

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Vanžurová, Alena. "Parallelisability conditions for differentiable three-webs." Archivum Mathematicum 031.1 (1995): 75-84. <http://eudml.org/doc/18424>.

@article{Vanžurová1995,
abstract = {Our aim is to find conditions under which a 3-web on a smooth $2n$-dimensional manifold is locally equivalent with a web formed by three systems of parallel $n$-planes in $\{R\}^\{2n\}$. We will present here a new approach to this “classical” problem using projectors onto the distributions of tangent subspaces to the leaves of foliations forming the web.},
author = {Vanžurová, Alena},
journal = {Archivum Mathematicum},
keywords = {distribution; projector; manifold; three-web; regular (parallelisable) web; 3-webs; Chern connection; parallelizability condition},
language = {eng},
number = {1},
pages = {75-84},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Parallelisability conditions for differentiable three-webs},
url = {http://eudml.org/doc/18424},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Vanžurová, Alena
TI - Parallelisability conditions for differentiable three-webs
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 1
SP - 75
EP - 84
AB - Our aim is to find conditions under which a 3-web on a smooth $2n$-dimensional manifold is locally equivalent with a web formed by three systems of parallel $n$-planes in ${R}^{2n}$. We will present here a new approach to this “classical” problem using projectors onto the distributions of tangent subspaces to the leaves of foliations forming the web.
LA - eng
KW - distribution; projector; manifold; three-web; regular (parallelisable) web; 3-webs; Chern connection; parallelizability condition
UR - http://eudml.org/doc/18424
ER -

References

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  16. On three-web manifolds, Report of the Czech Meeting 1993 on Incidence Structures, PU Olomouc, pp. 56–66. Zbl0794.53021
  17. On torsion of a three-web, ( to appear). 
  18. Almost-product structures, Differential geometry, Proc. of Symp. in Pure Math. vol. III, pp. 94-100. Zbl0103.38801MR0123993
  19. Matematika pro fyziky II, MFF UK, Praha, 1975. (1975) 
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  22. Differential invariants of webs on 2 -dimensional manifolds, Mat. Zametki 48, 26–37. MR1081890

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