A characterization of hermitian symmetric spaces of type IV by their automorphism group.
Abstract:
Let X be a complex manifold and let Aut(X) denote the group of holomorphic automorphisms of X. We say that X is characterized by its automorphism group if any complex manifold Y of the same dimension as X and such that Aut(Y ) is topologically isomorphic to Aut(X) is biholomorphic to X.
Let Ω be a bounded symmetric domain of type IV and dimension bigger than four. We show that a Stein manifold of the same dimension as Ω and with the same automorphism group is biholomorphic to Ω .
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