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arXiv · 2503.21881

Flat Generalized Connections on Courant Algebroids

Gil R. Cavalcanti·Jaime Pedregal·Roberto Rubio
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Abstract

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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Gil R. Cavalcanti, Jaime Pedregal, Roberto Rubio. 2025-03-27. Flat Generalized Connections on Courant Algebroids. https://doi.org/10.1007/s00029-025-01083-0

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