Bergman metrics as pull-backs of the Fubini-Study metric

2023/02/27 by Huang, Xiaojun, Li, Song-Ying
#32E10 #32F45 #32Q30 #53C25 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.13456

Abstract

Domains and more generally complex manifolds whose Bergman metrics have constant holomorphic sectional curvature are characterized. Our approach is to treat the Bergman metrics as the pull-back by the Bergman-Bochner maps of the Fubini-Study metric of the complex projective space of infinite dimension. Several new domains with surprising curvature properties for their Bergman metrics are constructed. A new conjecture is also formulated at the end of the paper.

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