Szabó’s algorithm and applications

Abstract

In this paper, Szabó’s algorithm is used as the main tool to find locally symmetric left invariant Riemannian metrics on some 4-dimensional Lie groups. Locally symmetric left invariant Riemannian Lie groups constitute an important subclass of Riemannian Lie groups with zero-divergence Weyl-tensor the so-called C-manifolds. Some properties of the curvature operator of these 4-dimensional C-manifolds are studied.