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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.

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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