Gray’s decomposition on doubly warped product manifolds and applications
Copyright policy )Gray’s decomposition on doubly warped product manifolds and applications
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.
Mathematics - Differential Geometry, FOS: Physical sciences, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Mathematical Physics (math-ph), doubly warped manifolds, Einstein-like manifolds, Codazzi Ricci tensor; doubly warped manifolds; Killing Ricci tensor; doubly warped space-times; Einstein-like manifolds;, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Special Riemannian manifolds (Einstein, Sasakian, etc.), Killing Ricci tensor, doubly warped spacetimes, Differential Geometry (math.DG), General geometric structures on manifolds (almost complex, almost product structures, etc.), Codazzi Ricci tensor, FOS: Mathematics, Applications of global differential geometry to the sciences, Mathematical Physics, 53C21, Secondary 53C50, 53C80
Mathematics - Differential Geometry, FOS: Physical sciences, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Mathematical Physics (math-ph), doubly warped manifolds, Einstein-like manifolds, Codazzi Ricci tensor; doubly warped manifolds; Killing Ricci tensor; doubly warped space-times; Einstein-like manifolds;, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Special Riemannian manifolds (Einstein, Sasakian, etc.), Killing Ricci tensor, doubly warped spacetimes, Differential Geometry (math.DG), General geometric structures on manifolds (almost complex, almost product structures, etc.), Codazzi Ricci tensor, FOS: Mathematics, Applications of global differential geometry to the sciences, Mathematical Physics, 53C21, Secondary 53C50, 53C80
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