About the Schouten-Weyl tensor on 3-dimensional Lorenzian Lie groups

2017/08/22 by Khromova, O. P., Klepikov, P. N., Klepikova, S. V. +1
#53C30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.06614

Abstract

The main purpose of this paper is to investigate the Schouten-Weyl tensor on the three-dimensional Lie groups with left-invariant Lorenzian metrics. The left-invariant Lorentzian metrics on the three-dimensional Lie groups with squared length zero Schouten-Weyl tensor are studied. Moreover, the three-dimensional metric Lie groups with almost harmonic (i.e. with zero curl and divergence) Schouten-Weyl tensor are investigated. In addition, the question about the harmonicity of contraction of the Schouten-Weyl tensor is considered.

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