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Left-Invariant Einstein-like Metrics on Compact Lie Groups

Author

Listed:
  • An Wu

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China)

  • Huafei Sun

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China)

Abstract

In this paper, we study left-invariant Einstein-like metrics on the compact Lie group G . Assume that there exist two subgroups, H ⊂ K ⊂ G , such that G / K is a compact, connected, irreducible, symmetric space, and the isotropy representation of G / H has exactly two inequivalent, irreducible summands. We prove that the left metric ⟨ · , · ⟩ t 1 , t 2 on G defined by the first equation, must be an A -metric. Moreover, we prove that compact Lie groups do not admit non-naturally reductive left-invariant B -metrics, such as ⟨ · , · ⟩ t 1 , t 2 .

Suggested Citation

  • An Wu & Huafei Sun, 2022. "Left-Invariant Einstein-like Metrics on Compact Lie Groups," Mathematics, MDPI, vol. 10(9), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1510-:d:807172
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