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On the fundamental group of compact homogeneous manifolds carrying an invariant fat distribution. (English) Zbl 1367.53046

The main result of the paper is the following: Let \(M=G/H\) be a homogeneous space of a compact Lie group \(G\). If \(M\) admits a \(G\)-invariant fat distribution, then \(\pi_1(M)\) is finite. The meaning of fatness is explained in the paper. Roughly, it is related to a property of the Levi-Tanaka form of the distribution. The key point in the proof is to show that the \(G\)-invariance of the fat distribution forces the Ricci tensor to be positive, so that (by homogeneity) Myer’s theorem implies that \(\pi_1(M)\) is finite.

MSC:

53C30 Differential geometry of homogeneous manifolds
58A30 Vector distributions (subbundles of the tangent bundles)
32V05 CR structures, CR operators, and generalizations
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References:

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