PreprintCC BY-NC-ND 4.0arXiv
Radial Projectively Induced Canonical Kähler Metrics: Rigidity and Classification
Abstract
We study radial Kähler metrics on domains of ℂn, n≥ 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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BibTeX
@misc{arezzo2026radial,
title = {{Radial Projectively Induced Canonical Kähler Metrics: Rigidity and Classification}},
author = {Claudio Arezzo and Andrea Loi and Giovanni Placini and Michela Zedda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08438},
eprint = {2609.08438},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08438},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Radial Projectively Induced Canonical Kähler Metrics: Rigidity and Classification
AU - Claudio Arezzo
AU - Andrea Loi
AU - Giovanni Placini
AU - Michela Zedda
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08438
UR - https://arxiv.org/abs/2609.08438
AB - We study radial Kähler metrics on domains of ℂ^n, n≥ 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.
ER -