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2nd-order symmetric Lorentzian manifolds I: characterization and general results

José M. M. Senovilla
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Abstract

The n-dimensional Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor (2-symmetric spacetimes) are characterized and classified. The main result is that either they are locally symmetric or they have a covariantly constant null vector field, in this case defining a subfamily of Brinkmann's class in n dimensions. Related issues and applications are considered, and new open questions presented.

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José M. M. Senovilla. 2008-10-24. 2nd-order symmetric Lorentzian manifolds I: characterization and general results. https://arxiv.org/abs/math/0604113

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