Some recent results on locally homogeneous compact spaces. (Quelques résultats récents sur les espaces localement homogènes compacts.) (French) Zbl 0861.53053

de Bartolomeis, Paolo (ed.) et al., Manifolds and geometry. Proceedings of a conference, held in Pisa, Italy, September 1993. Cambridge: Cambridge University Press. Symp. Math. 36, 267-283 (1996).
Let \(G\) be a Lie group, \(V=G/H\) a homogeneous space and \(M\) a compact manifold. The author recalls first the concept “\(M\) is locally modelled over \((V,g)\)” as a generalization of the property “\(M\) is a compact quotient of \(V\)”. Then he concentrates on two main problems: 1) Which are the homogeneous spaces on which compact manifolds can be locally modelled? 2) Which homogeneous spaces admit compact quotients? The author presents a survey of the recent essential contributions in this direction.
For the entire collection see [Zbl 0840.00037].
Reviewer: O.Kowalski (Praha)


53C30 Differential geometry of homogeneous manifolds
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry