Four-dimensional metric Lie groups with zero Schouten-Weyl tensor

DOI10.33048/SEMI.2019.16.019zbMath1412.53075OpenAlexW3015968526WikidataQ115222254 ScholiaQ115222254MaRDI QIDQ2633604

P. N. Klepikov

Publication date: 9 May 2019

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.33048/semi.2019.16.019

zbMATH Keywords

Lie groupsRicci operatorSegre typesSchouten-Weyl tensorleft-invariant (pseudo)Riemannian metrics

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Cites Work

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• Einstein-like pseudo-Riemannian homogeneous manifolds of dimension four
• Four-dimensional Lorentzian Lie groups
• Left-invariant Riemannian metrics on four-dimensional unimodular Lie groups with zero-divergence Weyl tensor
• Left-invariant Riemannian metrics on four-dimensional nonunimodular Lie groups with zero-divergence Weyl tensor
• Harmonic tensors on three-dimensional Lie groups with left-invariant Lorentz metric
• Einstein-like manifolds which are not Einstein
• Conformally flat homogeneous pseudo-Riemannian four-manifolds

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