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2013 | 11 | 12 | 2076-2088
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The automorphism groups of foliations with transverse linear connection

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EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
12
Strony
2076-2088
Opis fizyczny
Daty
wydano
2013-12-01
online
2013-10-08
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autor
Bibliografia
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  • [2] Besse A.L., Einstein Manifolds, Classics Math., Springer, Berlin, 2008
  • [3] Kamber F.W., Tondeur P., G-foliations and their characteristic classes, Bull. Amer. Math. Soc., 1978, 84(6), 1086–1124 http://dx.doi.org/10.1090/S0002-9904-1978-14546-7
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  • [6] Lewis A.D., Affine connections and distributions with applications to nonholonomic mechanics, In: Pacific Institute of Mathematical Sciences Workshop on Nonholonomic Constraints in Dynamics, Calgary, August 26–30, 1997, Rep. Math. Phys., 1998, 42(1-2), 135–164
  • [7] Macias-Virgós E., Sanmartín Carbón E., Manifolds of maps in Riemannian foliations, Geom. Dedicata, 2000, 79(2), 143–156 http://dx.doi.org/10.1023/A:1005217109018
  • [8] Michor P.W., Manifolds of Differentiable Mappings, Shiva Math. Ser., 3, Shiva, Nantwich, 1980
  • [9] Molino P., Propriétés cohomologiques et propriétés topologiques des feuilletages à connexion transverse projetable, Topology, 1973, 12, 317–325 http://dx.doi.org/10.1016/0040-9383(73)90026-8
  • [10] Molino P., Riemannian Foliations, Progr. Math., 73, Birkhäuser, Boston, 1988 http://dx.doi.org/10.1007/978-1-4684-8670-4
  • [11] Palais R.S., Foundations of Global Non-Linear Analysis, Benjamin, New York-Amsterdam, 1968
  • [12] Postnikov M.M., Lectures in Geometry V, Factorial, Moscow, 1998 (in Russian)
  • [13] Walker A.G., Connexions for parallel distributions in the large, Quart. J. Math. Oxford Ser., 1955, 6, 301–308 http://dx.doi.org/10.1093/qmath/6.1.301
  • [14] Willmore T.J., Connexions for systems of parallel distributions, Quart. J. Math. Oxford Ser., 1956, 7, 269–276 http://dx.doi.org/10.1093/qmath/7.1.269
  • [15] Zhukova N.I., Minimal sets of Cartan foliations, Proc. Steklov Inst. Math., 2007, 256(1), 105–135 http://dx.doi.org/10.1134/S0081543807010075
  • [16] Zhukova N.I., Global attractors of complete conformal foliations, Sb. Math., 2012, 203(3–4), 380–405 http://dx.doi.org/10.1070/SM2012v203n03ABEH004227
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0307-8
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