Complex submanifolds of the complex projective space with second fundamental form of constant length
Complex submanifolds of the complex projective space with second fundamental form of constant length
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具有等长第二基本形式的复射影空间的复子流形
DOI：
10.2996/kmj/1138845888
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发表时间：
1969
期刊：
影响因子：
--
通讯作者：
K. Ogiue
中科院分区：
文献类型：
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作者：
K. Ogiue
在最近的工作[1]Chern， do Carmo和Kobayashi建立了一个关于球的紧极小子流形的第二基本形式长度的捏缩问题，并对第二基本形式长度为一定常数的球的紧极小子流形进行了分类。在本文中，我们将给出一个复杂的模拟。设Pn+P(C)为复维数n+P的复射影空间，具有Fubini-Study度量。设M是Pn+P(C)的^维紧复子流形设h是第二个基本形式。我们用S表示h长度的平方，然后我们可以看到
In a recent work [1] Chern, do Carmo and Kobayashi have established a pinching problem, with respect to the length of the second fundamental form, for compact minimal submanifolds of a sphere and have classified compact minimal submanifolds of a sphere whose lengths of the second fundamental form are certain constants. In the present paper we shall give a complex analogue. Let Pn+P(C) be the complex projective space of complex dimension n+p with the Fubini-Study metric. Let M be an ^-dimensional compact complex submanifold of Pn+P(C) and let h be the second fundamental form. We denote by S the square of the length of h. Then we can see that