Geodesic
Closedness of the Tangent Spaces to the Orbits of Proper Actions
Journal of Lie theory, Tome 18 (2008) no. 3, pp. 517-521
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We show that for any proper action of a Banach-Lie group $G$ on a Banach manifold $M$, the corresponding tangent maps ${\frak g} \to T_x(M)$ have closed range for each $x \in M$, i.e., the tangent spaces of the orbits are closed. As a consequence, for each free proper action on a Hilbert manifold, the quotient $M/G$ carries a natural manifold structure.
Classification : 22E65, 58B25, 57E20
Mots-clés : Banach Lie group, Banach manifold, proper action 
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     author = {M. Jotz and K.-H. Neeb},
     title = {Closedness of the {Tangent} {Spaces} to the {Orbits} of {Proper} {Actions}},
     journal = {Journal of Lie theory},
     pages = {517--521},
     year = {2008},
     volume = {18},
     number = {3},
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M. Jotz; K.-H. Neeb. Closedness of the Tangent Spaces to the Orbits of Proper Actions. Journal of Lie theory, Tome 18 (2008) no. 3, pp. 517-521. http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a1/