Flat Generalized Connections on Courant Algebroids
Differential Geometry
2025-11-19 v2
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.
Cite
@article{arxiv.2503.21881,
title = {Flat Generalized Connections on Courant Algebroids},
author = {Gil R. Cavalcanti and Jaime Pedregal and Roberto Rubio},
journal= {arXiv preprint arXiv:2503.21881},
year = {2025}
}
Comments
34 pages. To appear in Selecta Mathematica, New Series