Turkish Journal of Mathematics
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.
Lie algebra, Lie group, locally symmetric metric, $Z$-decomposition, Weyl tensor
NGAHA, MICHEL BERTRAND DJIADEU; MBATAKOU, SALOMON JOSEPH; and PEFOUKEU, ROMAIN NIMPA
"Szabos algorithm and applications,"
Turkish Journal of Mathematics: Vol. 47:
4, Article 9.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss4/9