Asian Journal of Mathematics

Volume 23 (2019)

Number 4

Homogeneous Kobayashi-hyperbolic manifolds with high-dimensional group of holomorphic automorphisms

Pages: 585 – 608



Alexander Isaev (Mathematical Sciences Institute, Australian National University, Acton, Canberra, ACT, Australia)


We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n \geq 2$ whose holomorphic automorphism group has dimension $n^2 - 2$. This result complements an existing classification for automorphism group dimension $n^2 - 1$ and greater obtained without the homogeneity assumption.


Kobayashi-hyperbolic manifolds, homogeneous complex manifolds, group of holomorphic automorphisms

2010 Mathematics Subject Classification

32M05, 32M10, 32Q45

Received 1 February 2018

Accepted 23 March 2018

Published 7 January 2020