We introduce connection, torsion, and curvature for Courant algebroids. We discuss in detail torsionless connections compatible with a generalized metric and the related Einstein-Hilbert actions.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3946