On the automorphism groups of hyperbolic manifolds

1999/06/22 by Alexander Isaev, A. V. Isaev, Isaev, A. V. +3 · 5 citations
Mathematics · #32H02 #32H20 #32M05 #Advanced Combinatorial Mathematics #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.CV #math.DG #msc:32H02 #msc:32H20 #msc:32M05

paper · pdf · doi:10.48550/arxiv.math/9906142

15 pages, see also http://wwwmaths.anu.edu.au/research.reports/99mrr.html

arxiv created 1999/06/22 · openalex publication_date 1999/06/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there does not exist a Kobayashi hyperbolic complex manifold of dimension n≠ 3, whose group of holomorphic automorphisms has dimension n²+1 and that, if a 3-dimensional connected hyperbolic complex manifold has automorphism group of dimension 10, then it is holomorphically equivalent to the Siegel space. These results complement earlier theorems of the authors on the possible dimensions of automorphism groups of domains in comlex space. The paper also contains a proof of our earlier result on characterizing n-dimensional hyperbolic complex manifolds with automorphism groups of dimension ≥ n²+2.

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