准sasakian几何上的Riemann孤子

IF 1 Q1 MATHEMATICS
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
25 weeks
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