论文标题
在一类梯度上几乎是Ricci Solitons
On a Class of Gradient Almost Ricci Solitons
论文作者
论文摘要
在这项研究中，我们提供了一些分类的分类，该分类是lorentzian和中性签名中的$（m，g，f）$表示的几乎是ricci solitons，以$（m，g，f）$表示。首先，我们证明，如果$ || \ nabla f || $是一个非零的常数，则$（m，g，f）$是对$ i \times_φn $的{扭曲product}的本地等距，其中$ i \ subset \ subset \ subset \ subset \ mathbb {r} $ and $ n $属于Contand cartertal curvature colvature contal curvature。另一方面，如果$ || \ nabla f || = 0 $，然后是本地{Walker歧管}。然后，我们构建了一个4维稳定梯度$ f $的示例 - 中性签名中的最多Ricci soliton。最后，我们提供了具有标准静态空间度量标准的梯度RICCI孤子的更多物理应用。
In this study, we provide some classifications for half-conformally flat gradient $f$-almost Ricci solitons, denoted by $(M, g, f)$, in both Lorentzian and neutral signature. First, we prove that if $||\nabla f||$ is a non-zero constant, then $(M, g, f)$ is locally isometric to a {warped product} of the form $I \times_φ N$, where $I \subset \mathbb{R}$ and $N$ is of constant sectional curvature. On the other hand, if $||\nabla f|| = 0$, then it is locally a {Walker manifold}. Then, we construct an example of 4-dimensional steady gradient $f$-almost Ricci solitons in neutral signature. At the end, we give more physical applications of gradient Ricci solitons endowed with the standard static spacetime metric.
