On the Symmetric Einstein Equation for Three-Dimensional Lie Groups with Left-Invariant Riemannian Metric and Semi-Symmetric Connection

Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most homogeneous case. In this direction, famous ones are results by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov other At same time, studying little for case an arbitrary metric connection. is primarily due to fact that tensor not, generally speaking, symmetric.
 paper, we consider semisymmetric connections on 3-dimensional Lie groups left-invariant metric. For symmetric part tensor, equation studied. As result research carried out, classification corresponding obtained.
 Earlier P.N. Klepikov, O.P. Khromova, classical was studied, it proved if classical.
 The holds group (pseudo) semi-symmetric Then, either connection, curvature equal zero.