Classification of third-order symmetric Lorentzian manifolds

Abstract

Third-order symmetric Lorentzian manifolds, i.e. Lorentzian manifold with zero third derivative of the curvature tensor, are classified. These manifolds are exhausted by a special type of pp-waves, they generalize Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.

11 pages. arXiv admin note: text overlap with arXiv:1011.3439

References in corpus (5)

• Two-symmetric Lorentzian manifolds
• On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
• One component of the curvature tensor of a Lorentzian manifold
• Second-order symmetric Lorentzian manifolds
• Covariant derivative of the curvature tensor of pseudo-Kählerian manifolds