论文标题
总歧管的共形粪便承认了一个Ricci Soliton
Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton
论文作者
论文摘要
在本文中，我们研究了从Ricci孤子子到具有非平凡例子的Riemannian歧管的共形浸入。首先，我们研究O'Neill Tensor $ a $的某些属性。我们还发现，与具有不同假设不同假设的此类MAP的总歧管计算了ricci张量的必要条件，并计算出Ricci张量。此外，我们考虑了从Ricci Soliton到Riemannian歧管的共形浸入$ f：m \至n $，并获得了$ f $的纤维和基本歧管$ n $的必要条件，即Ricci Soliton，几乎是Ricci Soliton和Einstein。此外，我们发现矢量字段及其水平升降机的必要条件分别是$ n $和$（kerf_ ast）^\ bot，$。此外，我们计算了Ricci Soliton $ M $的标量曲率。最后，我们获得了$ f $和谐的必要条件。
In this paper, we study conformal submersions from Ricci solitons to Riemannian manifolds with non-trivial examples. First, we study some properties of the O'Neill tensor $A$ in the case of conformal submersion. We also find a necessary and sufficient condition for conformal submersion to be totally geodesic and calculate the Ricci tensor for the total manifold of such a map with different assumptions. Further, we consider a conformal submersion $F:M \to N$ from a Ricci soliton to a Riemannian manifold and obtain necessary conditions for the fibers of $F$ and the base manifold $N$ to be Ricci soliton, almost Ricci soliton and Einstein. Moreover, we find necessary conditions for a vector field and its horizontal lift to be conformal on $N$ and $(KerF_\ast)^\bot,$ respectively. Also, we calculate the scalar curvature of Ricci soliton $M$. Finally, we obtain a necessary and sufficient condition for $F$ to be harmonic.
