准sasakian几何上的Riemann孤子

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2022-11-17 DOI:10.15330/cmp.14.2.395-405
K. De, U. De
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引用次数: 1

摘要

本文的目的是研究三维拟sasakian流形上的几乎黎曼孤子和梯度几乎黎曼孤子。首先证明了如果$(g, Z,\lambda)$是拟sasakian流形$M^3$上的一个几乎黎曼孤子,那么当孤子向量$Z$具有恒定散度时,它就可以化为一个恒定截面曲率的黎曼孤子,并且$M^3$具有恒定截面曲率$-1$。此外,我们证明了如果$Z$与特征向量场$\xi$点共线,则$Z$是$\xi$的常数倍,流形具有恒定的截面曲率$-1$。此外,几乎黎曼孤子正在膨胀。进一步证明了若拟sasakian流形$M^3$允许梯度几乎Riemann孤子,则$M^3$局部等距于双曲空间$H^{3}(-1)$。最后,我们构造了一个例子来证明本文的一些结果。
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Riemann solitons on para-Sasakian geometry
The goal of the present article is to investigate almost Riemann soliton and gradient almost Riemann soliton on 3-dimensional para-Sasakian manifolds. At first, it is proved that if $(g, Z,\lambda)$ is an almost Riemann soliton on a para-Sasakian manifold $M^3$, then it reduces to a Riemann soliton and $M^3$ is of constant sectional curvature $-1$, provided the soliton vector $Z$ has constant divergence. Besides these, we prove that if $Z$ is pointwise collinear with the characteristic vector field $\xi$, then $Z$ is a constant multiple of $\xi$ and the manifold is of constant sectional curvature $-1$. Moreover, the almost Riemann soliton is expanding. Furthermore, it is established that if a para-Sasakian manifold $M^3$ admits gradient almost Riemann soliton, then $M^3$ is locally isometric to the hyperbolic space $H^{3}(-1)$. Finally, we construct an example to justify some results of our paper.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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