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Homogeneous Riemannian manifolds of positive Ricci curvature

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Abstract

We prove that a homogeneous effective spaceM=G/H, whereG is a connected Lie group andH⊂G is a compact subgroup, admits aG-invariant Riemannian metric of positive Ricci curvature if and only if the spaceM is compact and its fundamental group π1(M) is finite (in this case any normal metric onG/H is suitable). This is equivalent to the following conditions: the groupG is compact and the largest semisimple subgroupLG⊂G is transitive onG/H. Furthermore, ifG is nonsemisimple, then there exists aG-invariant fibration ofM over an effective homogeneous space of a compact semisimple Lie group with the torus as the fiber.

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Authors and Affiliations

  1. Omsk State University, USSR

    V. N. Berestovskii

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  1. V. N. Berestovskii
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Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 334–340, September, 1995.

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Berestovskii, V.N. Homogeneous Riemannian manifolds of positive Ricci curvature. Math Notes 58, 905–909 (1995). https://doi.org/10.1007/BF02304766

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  • DOI: https://doi.org/10.1007/BF02304766

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