This article is cited in 1 paper

Structure of function algebras on foliated manifolds

P. N. Ivanshin

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: We consider a manifold $M$ with a foliation $F$ given by a locally free action of a commutative Lie group $H$. Also we assume that there exists an integrable Ehresmann connection on $(M; F)$ invariant with respect to the action of the group $H$. We get the structure of the restriction of the algebra $C_0(M)$ to the leaves in three partial cases. Also we consider a classification of the quasiinvariant measures and means on the leaves of $F$.

Keywords: Foliation, groupoid, group action Ehresmann connection, quasiinvariant measure, leaf function, invariant metric.

Submitted by: M. A. Malakhaltsev
Received: 12.12.2003

Language: English

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