论文标题
抗Quasi-Sasakian歧管
Anti-quasi-Sasakian manifolds
论文作者
论文摘要
我们介绍并研究了一类几乎接触度量歧管的特殊类别，我们称之为抗Quasi-Sasakian（AQS）。在横向的类别中，Kähler几乎接触度量歧管$（M，φ，ξ，η，G）$，Quasi-Sasakian和Anti-Quasi-Sasakian歧管的特征分别由$φ$ -Invariance和$φ$ -Invariance和$φ$ -Invariance和$φ$ -Inc. Boothby-Wang类型定理允许在主圆圈上获得AQS结构，该结构在Kähler歧管上，并带有封闭的$（2,0）$ - 表单。我们表征具有恒定$ξ$ - 切片曲率等于$ 1 $的AQS歧管：他们承认，框架束的$ sp（n）\ times 1 $ - 还原，使得歧管横向超级kähler，带有第二个aqs结构和null sasakian $η$η$ -Iinterstein结构。我们表明，具有恒定截面曲率的AQ歧管必然是平坦的，并且Cokähler。最后，通过使用与扭转的度量连接，我们为AQS歧管提供了足够的条件，可以局部分解为Kähler歧管的Riemannian乘积和具有最大等级结构的AQS歧管。在同一假设下，$（m，g）$不能在本地对称。
We introduce and study a special class of almost contact metric manifolds, which we call anti-quasi-Sasakian (aqS). Among the class of transversely Kähler almost contact metric manifolds $(M,φ, ξ,η,g)$, quasi-Sasakian and anti-quasi-Sasakian manifolds are characterized, respectively, by the $φ$-invariance and the $φ$-anti-invariance of the $2$-form $dη$. A Boothby-Wang type theorem allows to obtain aqS structures on principal circle bundles over Kähler manifolds endowed with a closed $(2,0)$-form. We characterize aqS manifolds with constant $ξ$-sectional curvature equal to $1$: they admit an $Sp(n)\times 1$-reduction of the frame bundle such that the manifold is transversely hyperkähler, carrying a second aqS structure and a null Sasakian $η$-Einstein structure. We show that aqS manifolds with constant sectional curvature are necessarily flat and cokähler. Finally, by using a metric connection with torsion, we provide a sufficient condition for an aqS manifold to be locally decomposable as the Riemannian product of a Kähler manifold and an aqS manifold with structure of maximal rank. Under the same hypothesis, $(M,g)$ cannot be locally symmetric.
