Hyperbolic manifolds of dimension n with automorphism group of dimension n²-1

2005/03/23 by Alexander Isaev, A. V. Isaev, Isaev, A. V.
Mathematics · #Analytic and geometric function theory #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.CV #math.DG #msc:32M05 #msc:32M10 #msc:32Q45

paper · pdf · doi:10.48550/arxiv.math/0503471

Final version, to appear in the J. Geometric Analysis, 29 pages

arxiv created 2005/09/20 · arxiv updated 2009/12/01

Abstract

We consider complex Kobayashi-hyperbolic manifolds of dimension n≥ 2 for which the dimension of the group of holomorphic automorphisms is equal to n²-1. We give a complete classification of such manifolds for n≥ 3 and discuss several examples for n=2.

Related

• Hyperbolic n-dimensional manifolds with automorphism group of dimension n²
• Homogeneous Kobayashi-hyperbolic manifolds with high-dimensional group of holomorphic automorphisms
• Homogeneous Kobayashi-hyperbolic manifolds with automorphism group of\n subcritical dimension
• On the automorphism groups of hyperbolic manifolds
• Continuing the classification of homogeneous Kobayashi-hyperbolic manifolds with high-dimensional automorphism group