Complex n-dimensional manifolds with a real n^2-dimensional automorphism group

The main theorem of this article is a characterization of non compact simply connected complete Kobayashi hyperbolic complex manifold of dimension $n ≥ 2$ with real $n^2$-dimensional holomorphic automorphism group. Together with the earlier work of Isaev and Krantz, this yields a complete classification of the simply-connected, complete Kobayashi hyperbolic manifolds with $dim_R(Aut (M)) ≥ dimC_ (M)^2$.