Hamiltonian 2-forms in Kähler geometry, IV weakly Bochner-flat Kähler manifolds
Hamiltonian 2-forms in Kähler geometry, IV weakly Bochner-flat Kähler manifolds
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DOI：
10.4310/cag.2008.v16.n1.a3
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发表时间：
2005-11
影响因子：
0.7
通讯作者：
V. Apostolov;D. Calderbank;P. Gauduchon;Christina W. Tønnesen-Friedman
中科院分区：
文献类型：
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作者：
V. Apostolov;D. Calderbank;P. Gauduchon;Christina W. Tønnesen-Friedman
我们研究了弱Bochner-flat（WBF）度量的构造和分类（即，Kahler度量与共闭Bochner张量）。一个Kahler度量是WBF当且仅当它的“正规化”Ricci形式是一个哈密顿2-形式：这样的2-形式在以前的系列论文中介绍和研究。因此，WBF Kahler度量是极值的。我们在射影丛上构造了许多新的WBF度量的例子，得到了紧WBF Kahler 6-流形的一个分类，推广了前三位作者在弱自对偶Kahler 4-流形上的工作.的建设是独立的以前的文件在该系列中，但分类依赖于分类的紧凑Kahler流形与哈密尔顿2-形式
We study the construction and classification of weakly Bochner-flat (WBF) metrics (i.e., Kahler metrics with coclosed Bochner tensor) on compact complex manifolds. A Kahler metric is WBF if and only if its 'normalized' Ricci form is a hamiltonian 2-form: such 2-forms were introduced and studied in previous papers in the series. It follows that WBF Kahler metrics are extremal. We construct many new examples of WBF metrics on projective bundles and obtain a classification of compact WBF Kahler 6-manifolds, extending work by the first three authors on weakly selfdual Kahler 4-manifolds. The constructions are independent of previous papers in the series, but the classification relies on the classification of compact Kahler manifolds with a hamiltonian 2-form