Riemann solitons on para-Sasakian geometry

Author:

De K.ORCID,De U.C.

Abstract

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.

Publisher

Vasyl Stefanyk Precarpathian National University

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On Submanifolds as Riemann Solitons;Bulletin of the Malaysian Mathematical Sciences Society;2024-02-21

2. The Z‐Tensor on Almost Co‐Kählerian Manifolds Admitting Riemann Soliton Structure;Advances in Mathematical Physics;2024-01

3. Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds;International Electronic Journal of Geometry;2023-10-29

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