特殊Kaehler流形作为抛物球面的实现
Realisation of special Kaehler manifolds as parabolic spheres
摘要：
证明了任意单连通特殊Kaehler流形的正则浸入为抛物仿射超球面。作为应用，我们将抛物仿射超球与任何非退化的全纯函数联系起来。我们还证明了Calabi和Pogorelov关于抛物球面的一个经典结果在完备的特殊Kaehler流形上具有正定度量。
英文摘要：
We prove that any simply connected special Kaehler manifold admits a canonical immersion as a parabolic affine hypersphere. As an application, we associate a parabolic affine hypersphere to any nondegenerate holomorphic function. Also we show that a classical result of Calabi and Pogorelov on parabolic spheres implies Lu's theorem on complete special Kaehler manifolds with a positive definite metric.
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