Geodesic
Structure of function algebras on foliated manifolds
Lobachevskii journal of mathematics, Tome 14 (2004), pp. 39-54

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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: group action Ehresmann connection, quasiinvariant measure, leaf function, invariant metric.
Mots-clés : Foliation, groupoid 
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     author = {P. N. Ivanshin},
     title = {Structure of function algebras on foliated manifolds},
     journal = {Lobachevskii journal of mathematics},
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     publisher = {mathdoc},
     volume = {14},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2004_14_a4/}
}
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P. N. Ivanshin. Structure of function algebras on foliated manifolds. Lobachevskii journal of mathematics, Tome 14 (2004), pp. 39-54. http://geodesic.mathdoc.fr/item/LJM_2004_14_a4/