Palatini Variation in Generalized Geometry and String Effective Actions

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