On the group of foliation isometries

Abstract

The purpose of our paper is to introduce some topology on the group $G_F^{r}(M)$ of all $C^{r}$-isometries of foliated manifold $(M,F)$, which depends on a foliation $F$ and coincides with compact-open topology when $F$ is an $n$-dimensional foliation. If the codimension of $F$ is equal to $n$, convergence in our topology coincides with pointwise convergence, where $ n=\operatorname{dim}M.$ It is proved that the group $G_F^{r}(M)$ is a topological group with compact-open topology, where $r\geq{0}.$ In addition it is showed some properties of F-compact-open topology.

Full Text

Article Information

Title	On the group of foliation isometries
Source	Methods Funct. Anal. Topology, Vol. 15 (2009), no. 2, 195-200
MathSciNet	MR2553535
Copyright	The Author(s) 2009 (CC BY-SA)

Authors Information

A. Ya. Narmanov
Department of Geometry and Applied Mathematics, National University of Uzbekistan, Tashkent, 100174, Uzbekistan

A. S. Sharipov
Department of Geometry and Applied Mathematics, National University of Uzbekistan, Tashkent, 100174, Uzbekistan 

Citation Example

A. Ya. Narmanov and A. S. Sharipov, On the group of foliation isometries, Methods Funct. Anal. Topology 15 (2009), no. 2, 195-200.

BibTex

@article {MFAT435,
    AUTHOR = {Narmanov, A. Ya. and Sharipov, A. S.},
     TITLE = {On the group of foliation isometries},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {195-200},
      ISSN = {1029-3531},
  MRNUMBER = {MR2553535},
       URL = {http://mfat.imath.kiev.ua/article/?id=435},
}