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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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