On univalence of equivariant Riemann domains over the complexification of a non-compact, Riemannian symmetric space

Details On univalence of equivariant Riemann domains over the complexification of a non-compact, Riemannian symmetric space On univalence of equivariant Riemann domains over the complexification of a non-compact, Riemannian symmetric space

2006-12-06

arxiv.org/abs/math/0612169v2

Mathematics

Complex Variables

46 pages, no figures. v2: minor correction, references updated

Scientific paper

Let G/K be a non-compact, rank-one, Riemannian symmetric space and let G^C be the universal complexification of G. We prove that a holomorphically separable, G-equivariant Riemann domain over G^C / K^C is necessarily univalent, provided that G is not a covering of SL(2, R). As a consequence of the above statement one obtains a univalence result for holomorphically separable, G x K -equivariant Riemann domains over G^C. Here G x K acts on G^C by left and right translations. The proof of such results involves a detailed study of the G-invariant complex geometry of the quotient G^C / K^C, including a complete classification of all its Stein G-invariant subdomains.

Affiliated with

Also associated with

No associations

Rating

On univalence of equivariant Riemann domains over the complexification of a non-compact, Riemannian symmetric space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On univalence of equivariant Riemann domains over the complexification of a non-compact, Riemannian symmetric space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On univalence of equivariant Riemann domains over the complexification of a non-compact, Riemannian symmetric space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-16267