## 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)

### MSC:

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

### Keywords:

locally homogeneous space; compact manifold