Bergman spaces of natural G-manifolds

Giuseppe Della Sala; Joe J. Perez

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arXiv · 1205.5154

Bergman spaces of natural G-manifolds

Giuseppe Della Sala·Joe J. Perez

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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.

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Giuseppe Della Sala, Joe J. Perez. 2012-05-23. Bergman spaces of natural G-manifolds. https://arxiv.org/abs/1205.5154

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