具有四分之一对称度量联络的$α$ -余辛流形上的$\ast$ - $η$ -Ricci-Yamabe孤子
$\ast$-$η$-Ricci-Yamabe solitons on $α$-Cosymplectic manifolds with a quarter-symmetric metric connection
摘要：
本文的目的是研究$α$ -余辛流形上关于四分之一对称度量联络的某些类型的度量，如$*$-$η$ -Ricci-Yamabe孤子.进一步证明了允许四分之一对称度量联络的$α$ -余辛流形的一些曲率性质。本文给出了$α$ -余辛流形上当流形满足四分之一对称度量联络时孤子的性质。当孤子的势向量场$ξ$在四分之一对称度规连接下为梯度型时，由$*$ - $η$ -Ricci-Yamabe孤子方程得到了Laplace方程.其次，我们研究了当向量场为共形killing且允许四分之一对称度规联络时孤子的性质。最后，我们给出了一个关于四分之一对称度量联络的5维$α$ -共辛度量为$*$ - $η$ -Ricci-Yamabe孤子的例子来证明我们的结果.
英文摘要：
The goal of the present paper is to deliberate certain types of metric such as $*$-$η$-Ricci-Yamabe soliton on $α$-Cosymplectic manifolds with respect to quarter-symmetric metric connection. Further, we have proved some curvature properties of $α$-Cosymplectic manifolds admitting quarter-symmetric metric connection. Here, we have shown the characteristics of the soliton when the manifold satisfies quarter-symmetric metric connection on $α$-Cosymplectic manifolds. Later, we have acquired Laplace equation from $*$-$η$-Ricci-Yamabe soliton equation when the potential vector field $ξ$ of the soliton is of gradient type in terms of quarter-symmetric metric connection. Next, we have developed the nature of the soliton when the vector field is conformal killing admitting quarter-symmetric metric connection. Finally, we present an example of a 5-dimensional $α$-cosymplectic metric as a $*$-$η$-Ricci-Yamabe soliton with respect to a quarter-symmetric metric connection to prove our results.
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