Flat Generalized Connections on Courant Algebroids

• Gil R. Cavalcanti ^[1] ; Jaime Pedregal ^[1] ; Roberto Rubio ^[2]
  1. [1] Utrecht University

     Utrecht University

     Países Bajos

     
  2. [2] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01083-0
• Enlaces
  • Texto completo
• Resumen

  • We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones.

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