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

TL;DR

This paper classifies all connected homogeneous Kobayashi-hyperbolic manifolds of dimension n≥2 with a specific automorphism group dimension, filling a gap in the existing classification for high-dimensional automorphism groups.

Contribution

It provides a complete classification of homogeneous Kobayashi-hyperbolic manifolds with automorphism group dimension n^2-2, extending previous results for larger automorphism groups.

Findings

Classified all such manifolds for the specified automorphism group dimension.

Extended the existing classification framework to include the case n^2-2.

Complemented prior work on automorphism groups with dimension ≥ n^2-1.

Abstract

We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 2$ 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.