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Journal of Mathematical Sciences

, Volume 198, Issue 5, pp 505–545 | Cite as

Harmonic Tensors on Three-Dimensional Lie Groups with Left-Invariant Lorentz Metric

  • O. P. Gladunova
  • E. D. Rodionov
  • V. V. Slavskii
Article

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.

Keywords

Structure Constant Ricci Tensor Weyl Tensor Complex Conjugate Root Harmonic Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • O. P. Gladunova
    • 1
  • E. D. Rodionov
    • 1
  • V. V. Slavskii
    • 2
  1. 1.Altai State UniversityBarnaulRussia
  2. 2.Ugra State UniversityKhanty-MansiyskRussia

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