We study three-dimensional Lie groups with left-invariant Lorentz metric and almost harmonic (with zero curl and divergence) Schouten–Weyl tensor. Contracting the Schouten-Weyl tensor in an arbitrary direction, we introduce an antisymmetric 2-tensor and study the structure of three-dimensional Lie groups and algebras with left-invariant Riemann metric in which this tensor is harmonic. Bibliography: 8 titles.
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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 12, No. 1, 2012, pp. 29–73.
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Gladunova, O.P., Rodionov, E.D. & Slavskii, V.V. Harmonic Tensors on Three-Dimensional Lie Groups with Left-Invariant Lorentz Metric. J Math Sci 198, 505–545 (2014). https://doi.org/10.1007/s10958-014-1806-2
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DOI: https://doi.org/10.1007/s10958-014-1806-2