Szabos algorithm and applications

Authors: MICHEL BERTRAND DJIADEU NGAHA, SALOMON JOSEPH MBATAKOU, ROMAIN NIMPA PEFOUKEU

Abstract: In this paper, Szabos 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.

Keywords: Lie algebra, Lie group, locally symmetric metric, $Z$-decomposition, Weyl tensor

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