On higher covariant derivatives of the curvature tensors of Kählerian C-spaces
On higher covariant derivatives of the curvature tensors of Kählerian C-spaces
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关于 Kählerian C 空间曲率张量的更高协变导数
DOI：
10.1017/s0027763000020432
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发表时间：
1983
影响因子：
0.8
通讯作者：
Ryoichi Takagi
中科院分区：
文献类型：
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作者：
Ryoichi Takagi
紧致单连通复齐性流形简称为C-空间，H. C. Wang [12].一个C-空间被称为凯勒空间，如果它允许一个凯勒度量，使得一组等距作用在它上面。紧型的埃尔米特对称空间是凯勒C-空间的典型例子。设M是任意的Kählerian C-空间，R是它的曲率张量。M. Itoh [6]用李代数的语言表示了R，并研究了R的各种性质。本文研究R的高阶协变导数。
A compact simply connected complex homogeneous manifold is said briefly a C-space, which was completely classified by H. C. Wang [12]. A C-space is called to be Kählerian if it admits a Kählerian metric such that a group of isometries acts transitively on it. Hermitian symmetric spaces of compact type are typical examples of a Kählerian C-space. Let M be an arbitrary Kählerian C-space and R its curvature tensor. M. Itoh [6] expressed R in the language of Lie algebra and investigated various properties of R. In this paper, we study higher covariant derivatives of R.