Further steps towards classifying homogeneous Kobayashi-hyperbolic manifolds with high-dimensional automorphism group

TL;DR

This paper classifies certain high-dimensional homogeneous Kobayashi-hyperbolic manifolds based on the dimension of their automorphism groups, extending previous classification results for larger automorphism groups.

Contribution

It completes the classification of connected homogeneous Kobayashi-hyperbolic manifolds for automorphism group dimensions close to the maximal value, specifically for dimensions $n^2-4$, $n^2-5$, and $n^2-6$.

Findings

Classified manifolds with automorphism group dimension $n^2-4$, $n^2-5$, and $n^2-6$ for $n ge 4$.

Extended previous classifications for automorphism group dimensions $n^2-3$ and higher.

Provided a comprehensive list of manifolds fitting these automorphism group dimension criteria.

Abstract

We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 4$ whose group of holomorphic automorphisms has dimension either $n^2-4$, or $n^2-5$, or $n^2-6$. This paper continues a series of articles that achieve classifications for automorphism group dimension $n^2-3$ and greater.