Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold
Copyright policy )Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold
First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding. Moreover, the soliton is trivial (Einstein) if either (i) $V$ is a contact vector field, or (ii) the Reeb vector field $\xi$ leaves the scalar curvature invariant. Finally, it is shown that if the metric of a Kenmotsu manifold represents a gradient Ricci almost soliton, then it is $\eta$-Einstein and the soliton is expanding. We also exhibited some examples of Kenmotsu manifold that admit Ricci almost solitons.
kenmotsu manifold, многовид Кенмоцу, майже солітон Річчі, викривлений добуток, Kenmotsu manifold, Almost contact and almost symplectic manifolds, Ricci almost soliton, Special Riemannian manifolds (Einstein, Sasakian, etc.), ricci almost soliton, QA1-939, General geometric structures on manifolds (almost complex, almost product structures, etc.), Kenmotsu manifold, Ricci almost soliton, Warped product, warped product, Mathematics
kenmotsu manifold, многовид Кенмоцу, майже солітон Річчі, викривлений добуток, Kenmotsu manifold, Almost contact and almost symplectic manifolds, Ricci almost soliton, Special Riemannian manifolds (Einstein, Sasakian, etc.), ricci almost soliton, QA1-939, General geometric structures on manifolds (almost complex, almost product structures, etc.), Kenmotsu manifold, Ricci almost soliton, Warped product, warped product, Mathematics
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