Generalized connections and integrability

We characterize the integrability of various structures on Courant algebroids in terms of torsion-free generalized connections. The applications include generalized Kähler and generalized hyper-Kähler structures as particular examples. We do also give a spinorial characterization in the case of regular Courant algebroids. This is based on the theory of Dirac generating operators, for which we develop a new approach based on the geometric data encoding the regular Courant algebroid.

This is joint work with Liana David, see arXiv:1905.01977.