Two-symmetric Lorentzian manifolds

Abstract

We classify two-symmetric Lorentzian manifolds using methods of the theory of holonomy groups. These manifolds are exhausted by a special type of pp-waves and, like the symmetric Cahen-Wallach spaces, they have commutative holonomy.

11 pages, the final version

References in corpus (3)

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

Cited by in corpus (11)

• New examples of compact Weyl-parallel manifolds
• The metric structure of compact rank-one ECS manifolds
• Some applications of the Lorentzian holonomy algebras
• Classification of third-order symmetric Lorentzian manifolds
• Covariant derivative of the curvature tensor of pseudo-Kählerian manifolds
• Conformally flat Lorentzian manifolds with special holonomy groups
• Locally conformally flat Lorentzian quasi-Einstein manifolds
• Locally Conformally Flat Lorentzian Gradient Ricci Solitons
• Structure of second-order symmetric Lorentzian manifolds
• Simple conformally recurrent space-times are conformally recurrent PP-waves
• Three-dimensional conformally symmetric manifolds