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A necessary condition for the existence of compact Clifford-Klein forms of homogeneous spaces of reductive type. (English) Zbl 0799.53056
A compact Clifford-Klein form of a homogeneous space $$G/H$$ is defined as a quotient $$\Gamma\setminus G/H$$ where $$\Gamma$$ is a subgroup of $$G$$ acting properly discontinuously and freely on $$G/H$$ so that $$\Gamma\setminus G/H$$ is compact in the quotient topology. The problem stated in the title is studied here and two (rather technical) necessary conditions are proved for the existence of a compact Clifford-Klein form of a given $$G/H$$ of the reductive type.
Reviewer: O.Kowalski (Praha)

##### MSC:
 53C30 Differential geometry of homogeneous manifolds
##### Keywords:
homogeneous space; Clifford-Klein form; reductive type
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##### References:
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