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http://dx.doi.org/10.11568/kjm.2020.28.4.739

A NOTE ON ALMOST RICCI SOLITON AND GRADIENT ALMOST RICCI SOLITON ON PARA-SASAKIAN MANIFOLDS  

De, Krishnendu (Kabi Sukanta Mahavidyalaya)
De, Uday Chand (Department of Pure Mathematics, University of Calcutta)
Publication Information
Korean Journal of Mathematics / v.28, no.4, 2020 , pp. 739-751 More about this Journal
Abstract
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, λ) 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 λ=-2. Besides these, in this section, we prove that if V is pointwise collinear with ξ, then V is a constant multiple of ξ 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.
Keywords
3-dimensional para-Sasakian manifold; Almost Ricci soliton; Gradient almost Ricci soliton;
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