English

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

Complex Variables 2024-05-13 v2

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.

Keywords

Cite

@article{arxiv.2302.13456,
  title  = {Bergman metrics as pull-backs of the Fubini-Study metric},
  author = {Xiaojun Huang and Song-Ying Li},
  journal= {arXiv preprint arXiv:2302.13456},
  year   = {2024}
}