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Remarks on geometric structures on compact complex spaces. (English) Zbl 0756.32017
C. T. C. Wall [Topology 25, 119-153 (1986; Zbl 0602.57014)] made a study of locally homogeneous geometric structure on compact complex surfaces and, more generally, on closed smooth 4-manifolds. The author of the reviewed paper corrects an error in the treatment of hyperbolic manifolds in the paper by Wall, completes some proofs and includes his additional remarks.

##### MSC:
 32J15 Compact complex surfaces 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 57N13 Topology of the Euclidean $$4$$-space, $$4$$-manifolds (MSC2010) 53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) 53C30 Differential geometry of homogeneous manifolds 53C35 Differential geometry of symmetric spaces 32Q20 Kähler-Einstein manifolds 32M10 Homogeneous complex manifolds 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
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