2025/03/27 by Cavalcanti, Gil R., Pedregal, Jaime, Rubio, Roberto
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.21881
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.