On the automorphism groups of hyperbolic manifolds
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 $n^2+1$ and that, if a 3dimensional 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 comlex space. The paper also contains a proof of our earlier result on characterizing $n$dimensional hyperbolic complex manifolds with automorphism groups of dimension $\ge n^2+2$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:math/9906142
 Bibcode:
 1999math......6142I
 Keywords:

 Mathematics  Complex Variables;
 Mathematics  Differential Geometry;
 32H02;
 32H20;
 32M05
 EPrint:
 15 pages, see also http://wwwmaths.anu.edu.au/research.reports/99mrr.html