Palatini Variation in Generalized Geometry and String Effective Actions

Abstract: 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.