The automorphism groups of foliations with transverse linear connection

Nina Zhukova; Anna Dolgonosova

Open Mathematics (2013)

  • Volume: 11, Issue: 12, page 2076-2088
  • ISSN: 2391-5455

Abstract

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The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.

How to cite

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Nina Zhukova, and Anna Dolgonosova. "The automorphism groups of foliations with transverse linear connection." Open Mathematics 11.12 (2013): 2076-2088. <http://eudml.org/doc/269020>.

@article{NinaZhukova2013,
abstract = {The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.},
author = {Nina Zhukova, Anna Dolgonosova},
journal = {Open Mathematics},
keywords = {Foliation; Linear connection; Automorphism group; Foliated bundle; Infinite-dimensional Lie group; foliation; linear connection; automorphism group; foliated bundle; infinite-dimensional Lie group},
language = {eng},
number = {12},
pages = {2076-2088},
title = {The automorphism groups of foliations with transverse linear connection},
url = {http://eudml.org/doc/269020},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Nina Zhukova
AU - Anna Dolgonosova
TI - The automorphism groups of foliations with transverse linear connection
JO - Open Mathematics
PY - 2013
VL - 11
IS - 12
SP - 2076
EP - 2088
AB - The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.
LA - eng
KW - Foliation; Linear connection; Automorphism group; Foliated bundle; Infinite-dimensional Lie group; foliation; linear connection; automorphism group; foliated bundle; infinite-dimensional Lie group
UR - http://eudml.org/doc/269020
ER -

References

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