The automorphism groups of foliations with transverse linear connection

• Autorzy: Nina Zhukova , Anna Dolgonosova
• Języki publikacji: 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.

Słowa kluczowe

EN

Foliation; Linear connection; Automorphism group; Foliated bundle; Infinite-dimensional Lie group

Kategorie tematyczne

• 53C12: Foliations (differential geometric aspects)
• 58Bxx: Infinite-dimensional manifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 12
• Strony: 2076-2088

Daty

wydano

2013-12-01

online

2013-10-08

Twórcy

autor

Nina Zhukova

• Nizhny Novgorod State University

autor

Anna Dolgonosova

• Nizhny Novgorod State University

Bibliografia

• [1] Bel’ko I.V., Affine transformations of a transversal projectable connection of a manifold with a foliation, Math. USSRSb., 1983, 45, 191–204 http://dx.doi.org/10.1070/SM1983v045n02ABEH001003
• [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
• [4] Kobayashi S., Nomizu K., Foundations of Differential Geometry I, Interscience, New York-London, 1963
• [5] Kriegl A., Michor P.W., Aspects of the theory of infinite-dimensional manifolds, Differential Geom. Appl., 1991, 1(2), 159–176 http://dx.doi.org/10.1016/0926-2245(91)90029-9
• [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

Identyfikatory

DOI

10.2478/s11533-013-0307-8