发表机构
International Centre for Theoretical Physics; Dipartimento di Matematica Università di Cagliari; Università di Parma（国际理论物理中心; 卡利亚里大学数学系; 帕尔马大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究复射影空间中径向Kähler度量的分类，证明常数非负数量曲率情形对应Fubini-Study、平坦或广义Burns-Simanca度量，并给出Kähler-Einstein与极值度量的刚性结论。
AI 中文摘要
我们研究$\n\mathbb{C}^n$（$n\geq 2$）域上的径向Kähler度量，这些度量允许Kähler浸入到有限维或无限维复射影空间中。我们分类了具有常数非负数量曲率的那些度量：在坐标的线性变换下，它们是Fubini-Study度量的正整数倍、平坦度量，或者在复二维情形下，是广义Burns-Simanca度量。我们还证明了每个径向射影诱导的Kähler-Einstein度量具有常数全纯截面曲率，因此是Fubini-Study、平坦或复双曲度量。最后，我们证明径向无限射影诱导的极值Kähler度量具有无界最大径向域当且仅当它是数量平坦的。
英文摘要
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.
Comments25 pages, comments are welcome
