Hyperbolic 2–dimensional manifolds with 3–dimensional automorphism group

Isaev, Alexander V

doi:10.2140/gt.2008.12.643

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

Alexander V Isaev

Geometry & Topology 12 (2008) 643–711

DOI: 10.2140/gt.2008.12.643

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 $n \geq 2$ .

Keywords

Kobayashi-hyperbolic manifolds, holomorphic automorphism groups

Mathematical Subject Classification 2000

Primary: 32Q45, 32M05

References

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

Volume 12, issue 2 (2008)