PARA-KENMOTSU METRIC AS A π-RICCI SOLITON
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The purpose of the paper is to study of Para-Kenmotsu metric as a π-Ricci soliton. The paper is organized as follows: β’ If an π-Einstein para-Kenmotsu metric represents an π-Ricci soliton with flow vector field V, then it is Einstein with constant scalar curvature r = -2n(2n + 1). β’ If a para-Kenmotsu metric g represents an π-Ricci soliton with the flow vector field V being an infinitesimal paracontact transformation, then V is strict and the manifold is an Einstein manifold with constant scalar curvature r = -2n(2n + 1). β’ If a para-Kenmotsu metric g represents an π-Ricci soliton with non-zero flow vector field V being collinear with π, then the manifold is an Einstein manifold with constant scalar curvature r = -2n(2n + 1). Finally, we cited few examples to illustrate the results obtained.
Abstract
The purpose of the paper is to study of Para-Kenmotsu metric as a π-Ricci soliton. The paper is organized as follows: β’ If an π-Einstein para-Kenmotsu metric represents an π-Ricci soliton with flow vector field V, then it is Einstein with constant scalar curvature r = -2n(2n + 1). β’ If a para-Kenmotsu metric g represents an π-Ricci soliton with the flow vector field V being an infinitesimal paracontact transformation, then V is strict and the manifold is an Einstein manifold with constant scalar curvature r = -2n(2n + 1). β’ If a para-Kenmotsu metric g represents an π-Ricci soliton with non-zero flow vector field V being collinear with π, then the manifold is an Einstein manifold with constant scalar curvature r = -2n(2n + 1). Finally, we cited few examples to illustrate the results obtained.
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