A note on almost Ricci soliton and gradient almost Ricci soliton on para-Sasakian manifolds

• Published in: 한국수학논문집, 28(4) 2020, 28(4), , pp.739-751
• Main Authors: Krishnendu De, Uday Chand De
• Format: Article
• Language: English
• Subjects: 수학
• ISSN: 1976-8605; 2288-1433
• DOI: 10.11568/kjm.2020.28.4.739

The object of the offering exposition is to study almost Ricci soliton and gradient almost Ricci soliton in 3-dimensional para-Sasakian manifolds. At first, it is shown that if $(g, V,\lambda)$ be an almost Ricci soliton on a 3-dimensional para-Sasakian manifold $M$, then it reduces to a Ricci soliton and the soliton is expanding for $\lambda$=-2. Besides these, in this section, we prove that if $V$ is pointwise collinear with $\xi$, then $V$ is a constant multiple of $\xi$ and the manifold is of constant sectional curvature $-1$. Moreover, it is proved that if a 3-dimensional para-Sasakian manifold admits gradient almost Ricci soliton under certain conditions then either the manifold is of constant sectional curvature $-1$ or it reduces to a gradient Ricci soliton. Finally, we consider an example to justify some results of our paper. KCI Citation Count: 0