Gray’s decomposition on doubly warped product manifolds and applications
Hoda El-Sayied, Carlo Mantica, Sameh Shenawy, Noha Syied
Abstract
A. Gray presented an interesting O(n) invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what condition(s), does a factor manifold Mi,i = 1,2 of a doubly warped product manifold M =f2 M1 x f1 M2 lie in the same Einstein- like class of M? By imposing sufficient and necessary conditions on the warping functions, an inheritance property of each class is proved. As an application, Einstein-like doubly warped product space-times of type A,B or P are considered.
Topics & Concepts
MathematicsPure mathematicsCovariant derivativeTensor productCovariant transformationManifold (fluid mechanics)Property (philosophy)Product (mathematics)Invariant (physics)Class (philosophy)Ricci curvatureMathematical analysisType (biology)DecompositionGeometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchNoncommutative and Quantum Gravity Theories