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arXiv · 1905.03509

Isotropic quasi-Einstein manifolds

Miguel Brozos-Vázquez·Eduardo García-Río·Xabier Valle-Regueiro
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Abstract

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.

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Miguel Brozos-Vázquez, Eduardo García-Río, Xabier Valle-Regueiro. 2019-05-09. Isotropic quasi-Einstein manifolds. https://doi.org/10.1088/1361-6382%2Fab4f1b

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