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A differential geometric characterization of invariant domains of holomorphy

Gregor Fels — 1995

Annales de l'institut Fourier

Let G = K be a complex reductive group. We give a description both of domains Ω G and plurisubharmonic functions, which are invariant by the compact group, K , acting on G by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space M : = G / K . Such an invariant domain Ω with a smooth boundary is Stein if and only if the corresponding domain Ω M M is geodesically convex and the sectional curvature of its boundary S : = Ω M fulfills the condition K S ( E ) K M ( E ) + k ( E , n ) . The term k ( E , n ) is explicitly computable...

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...

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