Geodesic
Invariant metrics on $G$-spaces
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 449-466.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $X$ be a $G$-space such that the orbit space $X/G$ is metrizable. Suppose a family of slices is given at each point of $X$. We study a construction which associates, under some conditions on the family of slices, with any metric on $X/G$ an invariant metric on $X$. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and locally connected metric space.
Classification : 54E35, 54H15, 57S30
Keywords: G-space; invariant metric; slice 
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     author = {Hajduk, Bogus{\l}aw and Walczak, Rafa{\l}},
     title = {Invariant metrics on $G$-spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {449--466},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2003},
     mrnumber = {1983465},
     zbl = {1075.54506},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_2_a18/}
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Hajduk, Bogusław; Walczak, Rafał. Invariant metrics on $G$-spaces. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 449-466. http://geodesic.mathdoc.fr/item/CMJ_2003__53_2_a18/