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Space-time admitting generalized conharmonic curvature tensor. (English) Zbl 1502.53028

Summary: The object of the present paper is to study space-time admitting generalized conharmonic curvature tensor. In this paper, we have studied the basic algebraic properties of generalized conharmonic curvature tensor. Next, it is proved that a \(4\)-dimensional relativistic generalized conharmonic flat space-time is an Einstein space-time and it is of constant curvature. Moreover, it is of \(O\)-type. It is also observed that in a \(4\)-dimensional relativistic perfect fluid generalized conharmonically flat space-time following Einstein’s field equation in the absence of cosmological constant, energy momentum tensor is covariant constant. Finally, it is proved that a \(4\)-dimensional relativistic conservative generalized conharmonic space-time \(M\) with constant scalar function \(\psi\) is a GRW space-time.

MSC:

53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B20 Local Riemannian geometry
53C80 Applications of global differential geometry to the sciences
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References:

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