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Turkish Journal of Mathematics

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.

DOI

10.55730/1300-0098.3419

Keywords

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

First Page

1169

Last Page

1181

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