In this article, it has been observed that a unit Killing vector field ξ on an n-dimensional Riemannian manifold (M,g), influences its algebra of smooth functions C∞(M). For instance, if h is eigenfunction the Laplace operator Δ with eigenvalue λ, then ξ(h) also same eigenvalue. Additionally, Hessian Hh(ξ,ξ) function h∈C∞(M) defines self adjoint ⊡ξ and properties similar to most compact (M,g). ...

휂-Ricci solitons on Lorentzian 훽-Kenmotsu manifold are considered an manifolds satisfying certain curvature Conditions, R(ξ,X).S=0, S(ξ,X).R=0, W2(ξ,X).S=0,S(ξ,X).W2=0 We proved that in β-Kenmotsu (M,φ,ξ,η,푔). Then the existence of implies M is Einstein and if Ricci tensor satisfies, then steady. If condition 휇=0, 휆=0, which shows 휆is steady

The object of this article is to define and study the Clairaut semi-invariant ξ⊥ -Riemannian submersions (Csi-ξ⊥ submersions, In short) from Kenmotsu manifolds onto Riemannian manifolds. We obtain necessary sufficient condition for a ξ⊥-Riemannian submersion be Csi-ξ⊥-Riemannian submersion. also work out on some fundamental differential geometric properties these submersions. Moreover, we prese...

This paper aims to improve Hille oscillation criteria for the third-order functional dynamic equation p2(ξ)ϕγ2p1ξϕγ1yΔ(ξ)ΔΔ+a(ξ)ϕγy(g(ξ))=0, on an above-unbounded time scale T. The obtained results related contributions reported in literature without restrictive conditions scales. To demonstrate essential results, example is presented.

Proof of Theorem 4. For wa ∈ [c + ck, rck w−c ], we have the boundary equilibrium. From its definition, yb(ξ) is decreasing in wa (that is, dyb(ξ) dwa < 0) and yb(ξ) = μ + ξ + G−1( r−c−ck r ) when wa = c + ck. The total supply chain profit at the boundary equilibrium is Πtot(yb(ξ), yb(ξ), ξ) = rEmin(μ + ξ + , yb(ξ)) − (c + ck)y(ξ) from Equations (16) and (17). This function is concave and incre...