论文标题
在Ricci上，几乎是由保形矢量场引起的孤子
On Ricci almost solitons arising from conformal vector fields
论文作者
论文摘要
令$ \ Overline {m}^{n+1} $为恒定截面曲率的半射线歧管，并具有共形矢量字段。考虑一个riemannian歧管$ m^n $，在$ \ overline {m}^{n+1} $中浸入$ \ overline。考虑到这些假设，本文的最终目标是调查$ \ overline {m}^{n+1} $和RICCI几乎在$ m^n $上的soliton结构上的共形矢量字段之间的亲密关系。假设后一个歧管是连接的，并且完全脐带，我们可以自然地证明它是通过环境流形上共形矢量场的切向矢量场的几乎孤子结构的。这个结果本质上是相当普遍的，很少有具体的例子来说明其真正的力量。此外，考虑到Tashiro的定理，我们通过一类Riemannian Hypersurfaces的分类达到了本文的高潮，这些分类自然会通过在环境流形上存在一个形状的载体矢量领域来自然继承其RICCI几乎是Soliton结构。
Let $\overline{M}^{n+1}$ be a semi-Riemannian manifold of constant sectional curvature, and endowed with a conformal vector field . Consider a Riemannian manifold $M^n$, isometrically immersed into $\overline{M}^{n+1}$. With these hypotheses in mind, the ultimate goal of this paper is to investigate the intimate relationship between conformal vector fields on $\overline{M}^{n+1}$ and the Ricci almost soliton structure on $M^n$. Assuming that the latter manifold is connected and totally umbilic, we prove that it is naturally given a Ricci almost soliton structure by means of the tangential part of a conformal vector field on the ambient manifold. This result is rather general in nature, and few concrete examples are worked out to illustrate its true power. Furthermore, with Tashiro's theorem in mind, we reach the climax of this paper with a classification of a class of Riemannian hypersurfaces that naturally inherit their Ricci almost soliton structure by the existence of a conformal vector field on the ambient manifold.
