论文标题
浸入梯度几乎yamabe solitons中
Immersion of gradient almost Yamabe solitons into warped product manifolds
论文作者
论文摘要
本文的目的是研究梯度的几何形状，几乎是yamabe solitons浸入扭曲的产物歧管$ i \ times_ {f} m^{n} $的几何形状，其潜力由沉浸感的高度函数赋予。首先，由于扭曲产物歧管上的曲率条件，我们在紧凑型孤子子上提出了一些几何刚度。在续集中，我们研究了存在完全测量，完全脐带和最小孤子的条件。此外，在恒定角度浸入的范围内，旋转梯度的分类几乎是yamabe soliton浸入$ \ mathbb {r} \ times_ {f} \ mathbb {r}^{n} $的分类。
The purpose of this article is to study the geometry of gradient almost Yamabe solitons immersed into warped product manifolds $I\times_{f}M^{n}$ whose potential is given by the height function from the immersion. First, we present some geometric rigidity on compact solitons due to a curvature condition on the warped product manifold. In the sequel, we investigate conditions for the existence of totally geodesic, totally umbilical and minimal solitons. Furthermore, in the scope of constant angle immersions, a classification of rotational gradient almost Yamabe soliton immersed into $\mathbb{R}\times_{f}\mathbb{R}^{n}$ is also made.
