论文标题
肯莫茨流形的几乎$η$ -Ricci solitons
Almost $η$-Ricci solitons on Kenmotsu manifolds
论文作者
论文摘要
在本文中，我们将爱因斯坦的指标表征在此类更广泛的指标中，例如$η$ -RICCI solitons和$η$ -RICCI Solitons在Kenmotsu歧管上，并概括了其他作者的一些结果。首先，我们证明，如果是$η$ -IENSTEIN或潜在的矢量场$ v $是无限的接触转换或$ v $是与Reeb vector Field的无限接触转换，则为$η$ -Ricci Soliton是Einstein Metric。此外，我们证明，如果Kenmotsu歧管接收一个几乎$η$ -Ricci soliton，带有Reeb矢量场，而将标态曲率不变性留下，那么它是爱因斯坦的歧管。最后，我们介绍了$η$ -Ricci solitons和渐变$η$ -Ricci solitons的新示例，以说明我们的结果。
In this paper we characterize the Einstein metrics in such broader classes of metrics as almost $η$-Ricci solitons and $η$-Ricci solitons on Kenmotsu manifolds, and generalize some results of other authors. First, we prove that a Kenmotsu metric as an $η$-Ricci soliton is Einstein metric if either it is $η$-Einstein or the potential vector field $V$ is an infinitesimal contact transformation or $V$ is collinear to the Reeb vector field. Further, we prove that if a Kenmotsu manifold admits a gradient almost $η$-Ricci soliton with a Reeb vector field leaving the scalar curvature invariant, then it is an Einstein manifold. Finally, we present new examples of $η$-Ricci solitons and gradient $η$-Ricci solitons, which illustrate our results.
