论文标题
几乎关于Riemann Soliton和梯度的注释几乎是Riemann Soliton
A note on Almost Riemann Soliton and gradient almost Riemann soliton
论文作者
论文摘要
发行文章的追求是在非固定的正常触点折线$ m^3 $中调查\ emph {几乎riemann soliton}和\ emph {渐变{渐变几乎riemann soliton}。在其他所有方面，可以证明，如果$ m^3 $的度量是Riemann Soliton，带有无差异的潜在矢量场$ z $，那么歧管是Quasi-Sasakian，并且具有恒定的截面曲率 - $λ$，提供$α，$α，β= $常数。除此之外，还表明，如果$ m^3 $的度量是\ emph {ars}，而$ z $的指标与$ξ$ collinear colinear colinear colinear colinear，并且$ z $是$ξ$的常数倍数，则\ emph {arss}减少了riemann soliton，前提是$ a $ $α，convants \ constands \;β= $;此外，确定如果$ m^3 $带有$α，\; β= $常数允许梯度\ emph {ars} $（γ，ξ，λ）$，那么歧管是准撒萨基人，或者是恒定的截面曲率$ - （α^2-β^2）$。最后，我们开发了一个$ M^3 $的示例，承认了Riemann Soliton。
The quest of the offering article is to investigate \emph{almost Riemann soliton} and \emph{gradient almost Riemann soliton} in a non-cosymplectic normal almost contact metric manifold $M^3$. Before all else, it is proved that if the metric of $M^3$ is Riemann soliton with divergence-free potential vector field $Z$, then the manifold is quasi-Sasakian and is of constant sectional curvature -$λ$, provided $α,β=$ constant. Other than this, it is shown that if the metric of $M^3$ is \emph{ARS} and $Z$ is pointwise collinear with $ξ$ and has constant divergence, then $Z$ is a constant multiple of $ξ$ and the \emph{ARS} reduces to a Riemann soliton, provided $α,\;β=$constant. Additionally, it is established that if $M^3$ with $α,\; β=$ constant admits a gradient \emph{ARS} $(γ,ξ,λ)$, then the manifold is either quasi-Sasakian or is of constant sectional curvature $-(α^2-β^2)$. At long last, we develop an example of $M^3$ conceding a Riemann soliton.
