Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism group

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 $n\ge 2$.

77 pages

References in corpus (1)

• Effective actions of SU_n on complex n-dimensional manifolds

Cited by in corpus (7)

• Hyperbolic manifolds whose envelopes of holomorphy are not hyperbolic
• Proper actions of Lie groups of dimension $n^2+1$ on $n$-dimensional complex manifolds
• On the geometry of the symmetrized bidisc
• On the Kobayashi hyperbolicity of certain tube domains
• A characterization of the bidisc by a subgroup of its automorphism group
• Proper group actions in complex geometry
• Classical Symmetries of Complex Manifolds