论文标题
由有限或无限尺寸复杂空间诱导的极端Kaehler指标
Extremal Kaehler metrics induced by finite or infinite dimensional complex space forms
论文作者
论文摘要
在本文中，我们解决了研究那些配备有限或无限维尺寸复杂空间形式的$ g $的复杂歧管$ m $的问题。我们证明，当假定$ g $是径向并且环境空间为有限的维度时，$（m，g）$本身就是一个复杂的空间形式。我们通过施加最强的假设，即公制$ g $具有恒定的标态曲率并且行为良好（请参阅引言中的定义1），我们将此结果扩展到无限的维度设置。最后，我们分析了由无限尺寸椭圆形复杂空间诱导的径向kaehler-enstein指标，我们表明，如果假定这种度量可以满足稳定性条件，则被迫具有恒定的非阳性骨膜截面曲率。
In this paper we address the problem of studying those complex manifolds $M$ equipped with extremal metrics $g$ induced by finite or infinite dimensional complex space forms. We prove that when $g$ is assumed to be radial and the ambient space is finite dimensional then $(M, g)$ is itself a complex space form. We extend this result to the infinite dimensional setting by imposing the strongest assumption that the metric $g$ has constant scalar curvature and is well-behaved (see Definition 1 in the Introduction). Finally, we analyze the radial Kaehler-Einstein metrics induced by infinite dimensional elliptic complex space forms and we show that if such a metric is assumed to satisfy a stability condition then it is forced to have constant non-positive holomorphic sectional curvature.
