Three-dimensional semi-symmetric homogeneous Lorentzian manifolds
It is known that a locally homogeneous semi-symmetric Riemanian manifold (i.e. with \(R(X,Y)\cdot R=0)\) is locally symmetric (i.e. with \(\nabla R=0)\). The problem is, can this be extended to the pseudo-Riemannian case and in particular, to Lorentzian geometry. In the present paper there are found some three-dimensional homogeneous Lorentzian manifolds which are semi-symmetric but not symmetric. Also the complete classification of three-dimensional semi-symmetric homogeneous Lorentzian manifolds is obtained. In a forthcoming paper the author will classify the three-dimensional conformally flat semi-symmetric Lorentzian manifolds.
scientific article; zbMATH DE number 5651851