h-Ricci soliton and Gradient h-Ricci soliton on para-Kenmotsu manifold
Resumo
The current paper examines the h-Ricci soliton and gradient h-Ricci soliton on a para-Kenmotsu manifold when h has a definite signal. Firstly
we show that h-Ricci soliton on the present manifold is Einstein whenever the
potential vector field V is contact, and if the potential vector field V is collinear
with the Reeb vector field ξ, then the manifold is η-Einstein manifold. Next,
we prove that a η-Einstein para-Kenmotsu metric as an h-Ricci soliton reduces
to Einstein manifold. Finally, we show that a similar result occurs in the case
of gradient h-Ricci soliton.
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Referências
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