Homogeneous Kobayashi-hyperbolic manifolds with automorphism group of subcritical dimension

TL;DR

This paper classifies all connected homogeneous Kobayashi-hyperbolic manifolds of dimension n with automorphism groups of dimension n^2-3, filling a gap between known classifications at dimensions n^2-2 and higher.

Contribution

It provides a complete classification of such manifolds for the specific automorphism group dimension n^2-3, extending existing results.

Findings

Identifies all manifolds with automorphism group dimension n^2-3

Complements previous classifications for dimensions n^2-2 and above

Enhances understanding of the structure of Kobayashi-hyperbolic manifolds

Abstract

We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 2$ whose holomorphic automorphism group has dimension $n^2-3$. This result complements existing classifications for automorphism group dimension $n^2-2$ (which is in some sense critical) and greater.