We give the necessary and sufficient conditions for a gradient Ricci-Yamabe soliton with warped product metric. As physical applications, we consider solitons on generalized Robertson-Walker space-times standard static space-times.

Given a compact Riemannian manifold M , we consider a warped product M̄ = I ×h M where I is an open interval in R. We suppose that the mean curvature of the fibers do not change sign. Given a positive differentiable function ψ in M̄ , we find a closed hypersurface Σ which is solution of an equation of the form F (B) = ψ, where B is the second fundamental form of Σ and F is a function satisfying c...

A. Both bi-harmonic map and f -harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study f -bi-harmonic maps as the critical points of the f -bi-energy functional 1 2 ∫ M f |τ(φ)| dvg. This class of maps generalizes both concepts of harmonic maps and biharmonic maps. We first derive the f -biharmonic map ...

We prove an existence result for helicoidal graphs with prescribed mean curvature in a large class of warped product spaces which comprises space forms.

In the present note we study the existence or non-existence of doubly warped and doubly twisted product CR-submanifolds in nearly Kaehler manifolds.

In the present paper, we form a sharp inequality for doubly warped product submanifold of Riemannian manifold nearly quasi-constant curvature.