2nd-order symmetric Lorentzian manifolds I: characterization and general results
arXiv:math/0604113
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.
23 pages (in cqg format), no figures, one small table. Final corrections, references updated, proof of Corollary 3.1 improved, acknowledgements expanded. Version to be published in CQG