Geodesic
Compact homogeneous manifolds with integrable invariant distributions, and scalar curvature
Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 941-950

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It is proved that for a compact simply-connected effective homogeneous space $G/H$ of a connected compact Lie group $G$ by a closed subgroup $H$ the following conditions are equivalent: (1) Every $G$-invariant distribution on $G/H$ is integrable. (2) The space $G/H$ is of normal type in the sense of Bergery. (3) Every $G$-invariant Riemannian metric on $G/H$ has positive scalar curvature. (4) The space $G/H$ is isomorphic to a direct product of compact simplyconnected strongly isotropy-irreducible homogeneous spaces. 
@article{SM_1995_186_7_a1,
     author = {V. N. Berestovskii},
     title = {Compact homogeneous manifolds with integrable invariant distributions, and scalar curvature},
     journal = {Sbornik. Mathematics},
     pages = {941--950},
     publisher = {mathdoc},
     volume = {186},
     number = {7},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_7_a1/}
}
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V. N. Berestovskii. Compact homogeneous manifolds with integrable invariant distributions, and scalar curvature. Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 941-950. http://geodesic.mathdoc.fr/item/SM_1995_186_7_a1/