  We develop the Palatini formalism within the framework of generalized
Riemannian geometry of Courant algebroids. In this context, the Palatini
variation of a generalized Einstein-Hilbert-Palatini action - formed using a
generalized metric, a Courant algebroid connection (in contrary to the ordinary
case, not necessarily a torsionless one) and a volume form - leads naturally to
a proper notion of a generalized Levi-Civita connection and low-energy
effective actions of string theory.
