Ricci soliton and Ricci almost soliton on para-Kenmotsu manifold
Bull. Korean Math. Soc.
Published online May 29, 2019
Dhriti Sundar Patra
Birla Institute of Technology Mesra
Abstract : The purpose of this article is to study the Ricci soliton and Ricci almost soliton on para-Kenmotsu manifolds. 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 η-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 η-Einstein. This result is also hold for Ricci almost soliton if the potential vector field V is pointwise collinear with the Reeb vector field ξ.
Keywords : Ricci Soliton, Ricci almost soliton, Einstein manifold, paracontact metric manifold, para-Kenmotsu manifold
MSC numbers : 53C15; 53C25; 53D10; 53D15
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