Geodesic
Nonhomogeneous $G$-spaces of compact Lie groups
Matematičeskie zametki, Tome 13 (1973) no. 4, pp. 523-529 
M. Ya. Blinkin. Nonhomogeneous $G$-spaces of compact Lie groups. Matematičeskie zametki, Tome 13 (1973) no. 4, pp. 523-529. http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a5/
@article{MZM_1973_13_4_a5,
     author = {M. Ya. Blinkin},
     title = {Nonhomogeneous $G$-spaces of compact {Lie} groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {523--529},
     year = {1973},
     volume = {13},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a5/}
}
TY  - JOUR
AU  - M. Ya. Blinkin
TI  - Nonhomogeneous $G$-spaces of compact Lie groups
JO  - Matematičeskie zametki
PY  - 1973
SP  - 523
EP  - 529
VL  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a5/
LA  - ru
ID  - MZM_1973_13_4_a5
ER  - 
%0 Journal Article
%A M. Ya. Blinkin
%T Nonhomogeneous $G$-spaces of compact Lie groups
%J Matematičeskie zametki
%D 1973
%P 523-529
%V 13
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a5/
%G ru
%F MZM_1973_13_4_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

A duality theorem for a compact $G$-manifold $M$ of a compact Lie group $G$ is proved. For the case when all the orbits in $M$ are principal, it is proved that the quotient space of the complexification of $M$ by the action of the associated algebraic group $G^c$ is isomorphic to the quotient space of $M$ by the action of $G$.