Hodge and vanishing theorems on complex Finsler vector bundles
Hodge and vanishing theorems on complex Finsler vector bundles
复制标题
复数 Finsler 向量丛上的 Hodge 定理和消失定理
DOI：
10.1007/s12220-019-00256-6
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发表时间：
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影响因子：
1.1
通讯作者：
Tongde Zhong
中科院分区：
文献类型：
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作者：
Jinling Li;Chunhui Qiu;Tongde Zhong
在本文中，我们研究强赝凸复Finsler向量丛上的Hodge定理和消失定理。首先，我们给出了强赝凸复Finsler向量丛上各种拉普拉斯算子的定义，并得到了它们的Hodge定理。其次，我们推导了一些关于强赝凸复Finsler向量丛的有用公式，例如Bochner-Kodaira-Nakano恒等式和Siu在Hermitian向量丛上获得的Bochner-Kodaira技术。最后，我们证明了强伪凸复Finsler向量丛上的一些消失定理。特别是，在强赝凸复Berwald向量丛上，我们得到了上同调群的Hodge同构定理和消失定理。
In this paper, we study the Hodge and vanishing theorems on strongly pseudoconvex complex Finsler vector bundles. First, we give definitions of various Laplace operators on strongly pseudoconvex complex Finsler vector bundles and obtain the Hodge theorems about them. Second, we deduce some useful formulas on strongly pseudoconvex complex Finsler vector bundles, such as the Bochner–Kodaira–Nakano identity andBochner–Kodaira technique which is obtained by Siu on Hermitian vector bundles. Finally, we prove some vanishing theorems on strongly pseudoconvex complex Finsler vector bundles. In particular, on strongly pseudoconvex complex Berwald vector bundles, we get the Hodge isomorphism theorems and vanishing theorems for cohomology groups.