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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
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