Continuing the classification of homogeneous Kobayashi-hyperbolic manifolds with high-dimensional automorphism group

TL;DR

This paper extends the classification of homogeneous Kobayashi-hyperbolic manifolds by determining all such manifolds with automorphism groups of dimension n^2 - 7 or n^2 - 8, building on previous classifications for larger automorphism groups.

Contribution

It completes the classification of these manifolds for the specified automorphism group dimensions, filling gaps in the existing literature.

Findings

Classified all homogeneous Kobayashi-hyperbolic manifolds with automorphism group dimension n^2 - 7.

Classified all such manifolds with automorphism group dimension n^2 - 8.

Extended previous classifications for automorphism group dimensions n^2 - 6 and above.

Abstract

We classify all homogeneous Kobayashi-hyperbolic manifolds of dimension $n \ge 2$ whose group of holomorphic automorphisms has dimension either $n^2 - 7$ or $n^2 - 8.$ This paper continues the work of A. Isaev, who classified all such manifolds with automorphism group dimension $n^2 - 6$ and greater.