Bergman spaces of natural G-manifolds
Complex Variables
2012-05-24 v1
Abstract
Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G--> M-->X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point p in bM such that T_p(G) is contained in the complex tangent space of bM at p, then the Bergman space of M is large. Natural examples include the gauged G-complexifications of Heinzner, Huckleberry, and Kutzschebauch.
Keywords
Cite
@article{arxiv.1205.5154,
title = {Bergman spaces of natural G-manifolds},
author = {Giuseppe Della Sala and Joe J. Perez},
journal= {arXiv preprint arXiv:1205.5154},
year = {2012}
}
Comments
24 pages, no figures