On a Generalization of Kähler Geometry
On a Generalization of Kähler Geometry
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论卡勒几何的推广
DOI：
10.1142/9789812812834_0015
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发表时间：
1957
期刊：
影响因子：
--
通讯作者：
S. Chern
中科院分区：
文献类型：
--
作者：
S. Chern
到目前为止，研究紧致Kahler流形的同调性质最有效的工具是Hodge的调和积分或调和微分形式理论。调和微分形式的概念定义在任何可定向的黎曼流形上，可以简单地介绍如下：黎曼度量允许我们定义星星算子，它将p次微分形式转换为n-p次微分形式，n是流形的维数。从算子 * 和外微分算子d，我们引入算子
So far the most effective tool for the study of the homology properties of compact Kàhler manifolds is Hodge's theory of harmonic integrals or harmonic differential forms. The notion of a harmonic differential form is defined on any orientable Riemann manifold, and can be briefly introduced as follows: The Riemann metric allows us to define the star operator which transforms a differential form of degree p into one of degree n—p, n being the dimension of the manifold. From the operator* and the exterior differentiation operator d we introduce the operators