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Kyungpook Mathematical Journal 2019; 59(1): 149-161

Published online March 31, 2019

Copyright © Kyungpook Mathematical Journal.

Curvature Properties of η-Ricci Solitons on Para-Kenmotsu Manifolds

Abhishek Singh*, and Shyam Kishor

Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, Uttar Pradesh, India
e-mail : lkoabhi27@gmail.com and skishormath@gmail.com

Received: August 4, 2017; Accepted: October 23, 2018

Abstract

In the present paper, we study curvature properties of η-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of η-Ricci solitons on para-Kenmotsu manifolds satisfying R(ξ, X).C = 0, R(ξ, X). = 0, R(ξ, X).P = 0, R(ξ, X). = 0 and R(ξ, X).H = 0, where C, , P, and H are a quasi-conformal curvature tensor, a M-projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.

Keywords: η-Ricci solitons, almost paracontact structure, pseudo-projective curvature tensor, M-projective curvature tensor, conharmonic curvature tensor, quasi-conformal curvature tensor, concircular curvature tensor.