Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold
Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1315-1325
https://doi.org/10.4134/BKMS.b181175
Published online September 30, 2019
Dhriti Sundar Patra
Birla Institute of Technology Mesra
Abstract : The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field $V$ is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a $\eta$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is $\eta$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field $V$ is pointwise collinear with the Reeb vector field $\xi$.
Keywords : Ricci soliton, Ricci almost soliton, Einstein manifold, paracontact metric manifold, para-Kenmotsu manifold
MSC numbers : 53C15, 53C25, 53D10, 53D15
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