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Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.

Automorfismen. --- Hyperbolische ruimten. --- Hyperbolic spaces. --- Automorphisms. --- Espaces hyperboliques --- Automorphismes --- Electronic books. -- local. --- Probabilities. --- Topology. --- Hyperbolic spaces --- Automorphisms --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Probability --- Statistical inference --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Polyhedra --- Set theory --- Algebras, Linear --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential equations, partial. --- Partial differential equations --- Group theory --- Symmetry (Mathematics) --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean