Open Access

# 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.

### 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},
URL = {http://mfat.imath.kiev.ua/article/?id=435},
}