Abstract

AbstractIn this paper, we have studied space-time with \(W_6\)-curvature tensor and proved that a four-dimensional relativistic space-time M has conservative \(W_{6}\)-curvature tensor if and only if the energy-momentum tensor is Codazzi tensor provided that the scalar curvature is constant in both the cases. It is also observed that in a four-dimensional relativistic \(W_{6}\)-flat space-time satisfying Einstein’s field equation with cosmological constant, the energy-momentum tensor is covariant constant.Keywords\(W_6\)-curvature tensorConservative \(W_6\)-curvature tensorEinstein’s field equationPerfect fluid space-timeEnergy-momentum tensorGeneralized Robertson–Walker space-time2000 Mathematics Subject Classification53C2553C50Secondary 53C8053B20

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