In this paper, we consider Serrin’s overdetermined problems in warped product manifolds and prove type rigidity results by using the [Formula: see text]-function approach introduced Weinberger.

We find the necessary and sufficient conditions for a sequential warped product manifold to be quasi-Einstein manifold. also investigate standard static space-time generalized Robertson-Walker of quasi-constant curvature.

For the most general supersymmetric solutions of type IIB supergravity consisting of a warped product of AdS5 with a five-dimensional manifold M5, we construct an explicit consistent Kaluza-Klein reduction on M5 to minimal D = 5 gauged supergravity. Thus, any solution of the gauged supergravity can be uplifted on M5 to obtain an exact solution of type IIB supergravity. We also show that for gen...

Let (Mn,g) be a closed Riemannian manifold and N a warped product manifold of two space forms. We investigate geometric properties by the spectra of the Jacobi operator of a harmonic map φ : M → N . In particular, we show if N is a warped product manifold of Euclidean space with a space form and φ,ψ : M → N are two projectively harmonic maps, then the energy of φ and ψ are equal up to constant ...

In this paper, we give characterizations of a twisted product manifold to be a warped product manifold by imposing certain conditions on the Weyl conformal curvature tensor and the Weyl projective tensor. We also find similar results for multiply twisted product manifolds.