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The existence of some complex geometrical structures on a compact manifoldsuch as complex structures, Kaehler (pseudo-Kaehler) structures often imposecertain restrictions on its underling topological or differentiable manifold.In this article we survey recent developments in the study of the existence,classification and moduli problems of such structures on compact homogeneousmanifolds.

Complex and Kaehler structures on compact homogeneous manifolds - their existence, classification and moduli problem