Second-order symmetric Lorentzian manifolds: I. Characterization and general results

Details Second-order symmetric Lorentzian manifolds: I. Characterization and general results Second-order symmetric Lorentzian manifolds: I. Characterization and general results

Dec 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cqgra..25x5011s&link_type=abstract

Classical and Quantum Gravity, Volume 25, Issue 24, pp. 245011 (2008).

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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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