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

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

2006-04-05

arxiv.org/abs/math/0604113v4

Mathematics

Differential Geometry

23 pages (in cqg format), no figures, one small table. Final corrections, references updated, proof of Corollary 3.1 improved,

Scientific paper

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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