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Remarks on Homogeneous Complex Manifolds Satisfying Levi Conditions

Alan Huckleberry — 2010

Bollettino dell'Unione Matematica Italiana

Homogeneous complex manifolds satisfying various types of Levi conditions are considered. Classical results which were of particular interest to Andreotti are recalled. Convexity and concavity properties of flag domains are discussed in some detail. A precise classification of pseudoconvex flag domains is given. It is shown that flag domains which are in a certain sense generic are pseudoconcave.

Characterization of cycle domains via Kobayashi hyperbolicity

Gregor FelsAlan Huckleberry — 2005

Bulletin de la Société Mathématique de France

A real form G of a complex semi-simple Lie group G has only finitely many orbits in any given G -flag manifold Z = G / Q . The complex geometry of these orbits is of interest, e.g., for the associated representation theory. The open orbits D generally possess only the constant holomorphic functions, and the relevant associated geometric objects are certain positive-dimensional compact complex submanifolds of D which, with very few well-understood exceptions, are parameterized by the Wolf cycle domains Ω W ( D ) in...

On holomorphically separable complex solv-manifolds

Alan T. HuckleberryE. Oeljeklaus — 1986

Annales de l'institut Fourier

Let G be a solvable complex Lie group and H a closed complex subgroup of G . If the global holomorphic functions of the complex manifold X : G / H locally separate points on X , then X is a Stein manifold. Moreover there is a subgroup H ^ of finite index in H with π 1 ( G / H ^ ) nilpotent. In special situations (e.g. if H is discrete) H normalizes H ^ and H / H ^ is abelian.

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