On the Automorphism Groups of Hyperbolic Manifolds

Research Report MRR99-026

On the Automorphism Groups of Hyperbolic Manifolds

Alexander V. Isaev, Steven G. Krantz

Abstract: We show that there does not exist a Kobayashi hyperbolic complex manifold of dimension n\ne 3, whose group of holomorphic automorphisms has dimension n²+1 and that, if a 3-dimensional connected hyperbolic complex manifold has automorphism group of dimension 10, then it is holomorphically equivalent to the Siegel space. These results complement earlier theorems of the authors on the possible dimensions of automorphism groups of domains in complex space. The paper also contains a proof of our earlier result on characterizing n-dimensional hyperbolic complex manifolds with automorphism groups of dimensions \ge n²+2.

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