Complex space forms immersed in complex space forms
Complex space forms immersed in complex space forms
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复杂的空间形态沉浸在复杂的空间形态中
DOI：
10.1090/s0002-9947-1976-0407756-3
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发表时间：
1976
影响因子：
1.3
通讯作者：
K. Ogiue
中科院分区：
文献类型：
--
作者：
H. Nakagawa;K. Ogiue
我们确定了复空间形式到复空间形式的所有等距浸入。我们的结果可以看作是Calabi的一个著名结果的本地版本。具有常全纯曲率的Kaehler流形称为复空间型。所谓Kaehler子流形，是指具有诱导Kaehler度量的复子流形。E.Calabi(1)给出了完备和单连通复空间型的Kaehler嵌入到完备和单连通复空间型的分类。Calabi的结果的局部版本已被第二作者猜想为真(4)，并给出了部分解(2)、(3)。本文的目的是证明以下两个定理，它们为猜想提供了完整的解。在本文中，我们用Mn(C)表示具有常全纯曲率c的n维复空间形式。
We determine all the isometric immersions of complex space forms into complex space forms. Our result can be considered as the local version of a well-known result of Calabi. A Kaehler manifold of constant holomorphic curvature is called a complex space form. By a Kaehler submanifold we mean a complex submanifold with the induced Kaehler metric. E. Calabi (1) gave a classification of Kaehler im- beddings of complete and simply connected complex space forms into complete and simply connected complex space forms. The local version of Calabi's result has been conjectured to be true by the second author (4) and he gave some partial solutions (2), (3). The purpose of this paper is to prove the following two theorems which furnish the complete solutions to the conjecture. Throughout this paper we denote by Mn(c) an «-dimensional complex space form of constant holomorphic curvature c.