论文标题
几乎是肯莫托的棉花孤子3- $ h $ -manifolds
Cotton Solitons on Almost Kenmotsu 3-$h$-Manifolds
论文作者
论文摘要
在本文中，我们考虑了几乎肯莫茨（Kenmotsu）3- $ h $ manifolds的框架内的棉花孤子的概念。首先，我们认为潜在的矢量场是与Reeb载体场的近距离线性，并且证明了这种棉孤子的不存在。接下来，我们假设潜在的向量场与Reeb矢量场正交。事实证明，在非kenmotsu上的这种棉花孤子几乎是kenmotsu 3- $ h $ -manifold，使得reeb vector领域是RICCI操作员的特征向量，并且歧管在本地均等于$ \ \ \ \ mathbb {h}^2（h}^2（-4）\ times time \ times \ time \ mathbb bb} $。
In this paper, we consider the notion of Cotton soliton within the framework of almost Kenmotsu 3-$h$-manifolds. First we consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next we assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-$h$-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to $\mathbb{H}^2(-4) \times \mathbb{R}$.
