In this note, we characterize Sasakian manifolds endowed with ∗ - η -Ricci-Yamabe solitons. Also, the existence of ∗ - η -Ricci-Yamabe solitons in a 5-dimensional Sasakian manifold has been proved through a concrete example.

In the present paper, we characterize m-dimensional ζ-conformally flat LP-Kenmotsu manifolds (briefly, (LPK)m) equipped with the Ricci–Yamabe solitons (RYS) and gradient Ricci–Yamabe solitons (GRYS). It is proven that the scalar curvature r of an (LPK)m admitting an RYS satisfies the Poisson equation Δr=4(m−1)δ{β(m−1)+ρ}+2(m−3)r−4m(m−1)(m−2), where ρ,δ(≠0)∈R. In this sequel, the condition for which the scalar curvature of an (LPK)m admitting an RYS holds the Laplace equation is established. We also give an affirmative answer for the existence of a GRYS on an (LPK)m. Finally, a non-trivial example of an LP-Kenmotsu manifold (LPK) of dimension four is constructed to verify some of our results.

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Sasakian Manifolds Admitting ∗ - η -Ricci-Yamabe Solitons

ζ-Conformally Flat LP-Kenmotsu Manifolds and Ricci–Yamabe Solitons

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of 🟉-η-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results.

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Certain Curvature Conditions on Kenmotsu Manifolds and ★-η;-Ricci Solitons

. In this research article, we study ∗ - η -Ricci-Yamabe solitons on an α -Cosympletic manifold and show that it is η -Einstein manifold. In addition, we investigate that an α -Cosympletic manifold admitting ∗ - η -Ricci-Yamabe solitons satisﬁes some conditions. Lastly, we discuss the concircular, conformal, conharmonic, and W 2 -curvatures on the said manifold admitting ∗ - η -Ricci-Yamabe solitons.

CURVATURE PROPERTIES ON α -COSYMPLETIC MANIFOLDS WITH ∗ - η -RICCI-YAMABE SOLITONS

. In the current note, we study Lorentzian para-Kenmotsu (in brief, LP -Kenmotsu) manifolds admitting Ricci-Yamabe solitons (RYS) and gradient Ricci-Yamabe soliton (gradient RYS). At last by constructing a 5-dimensional non-trivial example we illustrate our result.

A note on $LP$-Kenmotsu manifolds admitting Ricci-Yamabe solitons

Transportation of sediment is an important and frequent phenomenon in rivers. Sediment is mobilized as bed-load with particles sliding, saltating, and rolling over the river bed, or as a suspended-load, where particles move with the turbulent water flow away from the bed.

Sediment Transport and Movable Bed s

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Three-manifolds with positive Ricci curvature

Contact manifolds.- Almost contact manifolds.- Geometric interpretation of the contact condition.- K-contact and sasakian structures.- Sasakian space forms.- Non-existence of flat contact metric structures.- The tangent sphere bundle.

Sasakian Manifolds Admitting ∗ - η -Ricci-Yamabe Solitons

Citations

ζ-Conformally Flat LP-Kenmotsu Manifolds and Ricci–Yamabe Solitons

Certain Curvature Conditions on Kenmotsu Manifolds and ★-η;-Ricci Solitons

CURVATURE PROPERTIES ON α -COSYMPLETIC MANIFOLDS WITH ∗ - η -RICCI-YAMABE SOLITONS

A note on $LP$-Kenmotsu manifolds admitting Ricci-Yamabe solitons

References

Sediment Transport and Movable Bed s

Three-manifolds with positive Ricci curvature

Contact manifolds in Riemannian geometry

Integral formulas in Riemannian geometry

Some Theorems on Ricci‐Recurrent Spaces