Korean J. Math. Vol. 29 No. 4 (2021) pp.705-714
DOI: https://doi.org/10.11568/kjm.2021.29.4.705

$\eta$-Ricci solitons on Para-Kenmotsu manifolds with some curvature conditions

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Published: Dec 30, 2021
Keywords:
Ricci solitons, $\eta$-Ricci solitons, para-Kenmotsu manifolds, Codazzi type of the Ricci tensor, Einstein manifold
Mathematics Subject Classification:
53C21, 53C25, 53C15.

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Ashis Mondal
Department of Mathematics, Jangipur College, Murshidabad

Abstract

In the present paper, we study $\eta$-Ricci solitons on para-Kenmotsu manifolds with Codazzi type of the Ricci tensor. We study $\eta$-Ricci solitons on para-Kenmotsu manifolds with cyclic parallel Ricci tensor. We also study $\eta$-Ricci solitons on $\varphi$-conformally semi-symmetric, $\varphi$-Ricci symmetric and conformally Ricci semi-symmetric para-Kenmotsu manifolds. Finally, we construct an example of a three-dimensional para-Kenmotsu manifold which admits $\eta$-Ricci solitons.



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