Geodesic
Homogeneous Riemannian manifolds of positive Ricci curvature
Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 334-340 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that a homogeneous effective space $M=G/H$, where $G$ is a connected Lie group and $H\subset G$ is a compact subgroup, admits a $G$-invariant Riemannian metric of positive Ricci curvature if and only if the space $M$ is compact and its fundamental group $\pi_1(M)$ is finite (in this case any normal metric on $G/H$ is suitable). This is equivalent to the following conditions: the group $G$ is compact and the largest semisimple subgroup $LG\subset G$ is transitive on $G/H$. Furthermore, if $G$ is nonsemisimple, then there exists a $G$-invariant fibration of $M$ over an effective homogeneous space of a compact semisimple Lie group with the torus as the fiber. 
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     author = {V. N. Berestovskii},
     title = {Homogeneous {Riemannian} manifolds of positive {Ricci} curvature},
     journal = {Matemati\v{c}eskie zametki},
     pages = {334--340},
     year = {1995},
     volume = {58},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a1/}
}
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V. N. Berestovskii. Homogeneous Riemannian manifolds of positive Ricci curvature. Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 334-340. http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a1/

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