论文标题
由偏斜形代数的连接诱导的对称托架引起的对称托架
Symmetric brackets induced by connections with totally skew-symmetric torsion on skew-symmetric algebroids
论文作者
论文摘要
在本说明中，我们讨论了与度量结构相关的偏斜形式代数的对称括号。给定伪 - 利曼式公制结构，我们描述了由谎言衍生物和函数差异语言完全偏斜的对称扭转引起的对称括号。特别是，我们获得了Levi-Civita连接的明确公式。我们还在几乎荒米利亚的流形上展示了一些对称括号。尤其是，我们讨论了第一个规范的Hermitian连接，并在使用对称括号的属性的情况下显示了几乎Kaehler歧管的情况。
In this note, we discuss symmetric brackets on skew-symmetric algebroids associated with a metric structure. Given a pseudo-Riemannian metric structure, we describe symmetric brackets induced by connections with totally skew-symmetric torsion in the language of Lie derivatives and differentials of functions. In particular, we obtain an explicit formula of the Levi-Civita connection. We also present some symmetric brackets on almost Hermitian manifolds. Especially, we discuss the first canonical Hermitian connection and show the formula for it in the case of nearly Kaehler manifolds using the properties of symmetric brackets.
