Two-symmetric Lorentzian manifolds

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.

► We classify two-symmetric Lorentzian manifolds using methods of the theory of holonomy groups. ► Two-symmetric Lorentzian manifolds are exhausted by a special type of pp-waves. ► Two-symmetric Lorentzian manifolds have commutative holonomy algebra.