We discuss Levi-Civita connections on Courant algebroids. We define an
appropriate generalization of the curvature tensor and compute the
corresponding scalar curvatures in the exact and heterotic case, leading to
generalized (bosonic) Einstein-Hilbert type of actions known from supergravity.
In particular, we carefully analyze the process of the reduction for the
generalized metric, connection,
... [Show full abstract] curvature tensor and the scalar curvature.
