#### Volume 12, issue 2 (2008)

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Hyperbolic $2$–dimensional manifolds with $3$–dimensional automorphism group

### Alexander V Isaev

Geometry & Topology 12 (2008) 643–711
##### Abstract

In this paper we determine all Kobayashi-hyperbolic 2–dimensional complex manifolds for which the group of holomorphic automorphisms has dimension 3. This work concludes a recent series of papers by the author on the classification of hyperbolic $n$–dimensional manifolds, with automorphism group of dimension at least ${n}^{2}-1$, where $n\ge 2$.

##### Keywords
Kobayashi-hyperbolic manifolds, holomorphic automorphism groups
##### Mathematical Subject Classification 2000
Primary: 32Q45, 32M05
##### Publication
Received: 17 November 2006
Accepted: 19 January 2008
Published: 12 May 2008
Proposed: Yasha Eliashberg
Seconded: Walter Neumann, Leonid Polterovich
##### Authors
 Alexander V Isaev Department of Mathematics The Australian National University Canberra, ACT 0200 Australia http://www.maths.anu.edu.au/~isaev