论文标题
关于Sasakian结构的刚性和余弦歧管的表征
On the rigidity of the Sasakian structure and characterization of cosymplectic manifolds
论文作者
论文摘要
我们在平滑的歧管（称为“弱”结构）上介绍新的度量结构，该结构将几乎接触，sasakian，cosymplectic等概括。公制结构$（φ，ξ，η，g）$，并允许我们对经典理论进行新的了解。我们通过概括了几个众所周知的结果来证明这一说法。我们证明，任何Sasakian结构都是刚性的，即我们弱的Sasakian结构在同质上等同于Sasakian结构。我们表明，具有平行张量$φ$的弱接触结构是一个弱的固定结构，并在歧管产物上给出了这样的结构的例子。我们发现矢量场是弱接触式无穷小变化的条件。
We introduce new metric structures on a smooth manifold (called "weak" structures) that generalize the almost contact, Sasakian, cosymplectic, etc. metric structures $(φ,ξ,η,g)$ and allow us to take a fresh look at the classical theory. We demonstrate this statement by generalizing several well-known results. We prove that any Sasakian structure is rigid, i.e., our weak Sasakian structure is homothetically equivalent to a Sasakian structure. We show that a weak almost contact structure with parallel tensor $φ$ is a weak cosymplectic structure and give an example of such a structure on the product of manifolds. We find conditions for a vector field to be a weak contact infinitesimal transformation.
