arXiv 2201.126542022-01-29math.DG

共形向量场中的Ricci几乎孤子

On Ricci almost solitons arising from conformal vector fields

Jose N. V. Gomes, Joao F. B. Pereira, Dragomir M. Tsonev

备注：: 21 pages

摘要：

设$\overline{M}^{n+1}$是具有常截面曲率的半黎曼流形，赋以共形向量场.考虑一个黎曼流形$M^n$，等距浸入$\overline{M}^{n+1}$。基于这些假设，本文的最终目的是研究$\overline{M}^{n+1}$上的共形向量场与$M^n$上的Ricci几乎孤子结构之间的密切关系.假设后一个流形是连通的且全脐的，我们证明了它是由其周围流形上共形向量场的切向部分自然地给出的Ricci几乎孤子结构.这个结果在本质上是相当一般的，并且很少有具体的例子来说明它的真正力量。此外，考虑到田代定理，我们达到了本文的高潮一类黎曼超曲面，自然继承其Ricci几乎孤子结构的存在下，一个共形向量场的环境流形的分类。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文