Curvature identities on almost Hermitian manifolds and applications

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• 作者：ChengJie Yu
• 关键词：almost Hermitian manifold ; canonical connection ; integrability
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：60
• 期：2
• 页码：285-300
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold. Moreover, we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection. As applications of the curvature identities, we obtain some results about the integrability of quasi Kähler manifolds and nearly Kähler manifolds.