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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...

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