Isotropic quasi-Einstein manifolds

Isotropic quasi-Einstein manifolds

We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the potential function preserves this harmonicity then, in the isotropic case, the manifold is necessarily a pp-wave. Using...

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Veröffentlicht in:Classical and quantum gravity 2019-12, Vol.36 (24), p.245005
Hauptverfasser: Brozos-Vázquez, M, García-Río, E, Valle-Regueiro, X
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harmonic Weyl tensor
quasi-Einstein equation
warped product
wave
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creator Brozos-Vázquez, M
García-Río, E
Valle-Regueiro, X
description We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the potential function preserves this harmonicity then, in the isotropic case, the manifold is necessarily a pp-wave. Using the quasi-Einstein equation, further conclusions are obtained for pp-waves. In particular, we show that a four-dimensional pp-wave is conformally Einstein if and only if it is locally conformally flat or has harmonic Weyl tensor.
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subjects harmonic Weyl tensor
quasi-Einstein equation
warped product
wave
title Isotropic quasi-Einstein manifolds
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