OpenAlex ·
Radial Projectively Induced Canonical Kähler Metrics: Rigidity and Classification
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.08438
- Original
- Read it at the publisher
- Topics
Abstract
We study radial Kähler metrics on domains of $\mathbb{C}^n$, $n\geq 2$, admitting a Kähler immersion into a finite- or infinite-dimensional complex projective space. We classify those with constant non-negative scalar curvature: up to a linear change of coordinates, they are positive integer multiples of the Fubini-Study metric, the flat metric, or, in complex dimension two, generalized Burns-Simanca metrics. We also prove that every radial projectively induced Kähler-Einstein metric has constant holomorphic sectional curvature and is therefore a Fubini-Study, flat, or complex hyperbolic metric. Finally, we show that a radial infinitely projectively induced extremal Kähler metric has unbounded maximal radial domain if and only if it is scalar-flat.
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