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 $n\ge 2$.