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Uniruled projective manifolds with irreducible reductive $$G$$-structures. (English) Zbl 0882.22007
Let $$G\subset GL(V)$$ be an irreducible faithful representation of a connected reductive complex Lie group $$G$$ on a vector space $$V$$. We show that if a uniruled projective manifold has a $$G$$-structure, then it must be a flat $$G$$-structure, and if $$G\neq GL(V)$$, the manifold is biholomorphic to an irreducible Hermitian symmetric space of the compact type. This gives an algebro-geometric characterization of Hermitian symmetric spaces of compact type without the assumption of homogeneity.

##### MSC:
 22E10 General properties and structure of complex Lie groups 53C35 Differential geometry of symmetric spaces 32M05 Complex Lie groups, group actions on complex spaces
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