In:
Carpathian Mathematical Publications, Vasyl Stefanyk Precarpathian National University, Vol. 14, No. 2 ( 2022-11-17), p. 395-405
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.
Type of Medium:
Online Resource
ISSN:
2313-0210
,
2075-9827
DOI:
10.15330/cmp.14.2.395-405
Language:
Unknown
Publisher:
Vasyl Stefanyk Precarpathian National University
Publication Date:
2022
detail.hit.zdb_id:
2801051-6
