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Uzbekistan Tashkent
Section Mathematics
Title On the group of diffeomorphisms of foliated manifolds
Author(-s) Narmanov A.Ya.a, Zoyidov A.N.a
Affiliations National University of Uzbekistana
Abstract Now the foliations theory is intensively developing branch of modern differential geometry, there are numerous researches on the foliation theory. The purpose of our paper is study the structure of the group $Diff_{F}(M)$ of diffeomorphisms and the group $Iso_{F}(M)$ of isometries of foliated manifold $(M,F)$. It is shown the group $Diff_{F}(M)$ is closed subgroup of the group $Diff(M)$ of diffeomorphisms of the manifold $M$ in compact-open topology and also it is proven the group $Iso_{F}(M)$ is Lie group. It is introduced new topology on $Diff_{F}(M)$ which depends on foliation $F$ and called $F$- compact open topology. It's proven that some subgroups of the group $Diff_F(M)$ are topological groups with $F$-compact open topology.
Keywords manifold, foliation, group of diffeomorphisms, compact open topology
UDC 517.977
MSC 22A05, 54H15, 57R50
DOI 10.35634/vm200104
Received 1 February 2020
Language English
Citation Narmanov A.Ya., Zoyidov A.N. On the group of diffeomorphisms of foliated manifolds, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 1, pp. 49-58.
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