Generalized geometry applied to 4d-supergravity

Generalized complex geometry is an example of a powerful formalism to attempt the construction of a language adequate to string theory. With the remarkable property of unifying symplectic and complex manifolds as special cases of a broader structure it is proving to be the right tool to use when trying to describe T-duality. The key idea was to look at both geometries as operations in the direct sum of tangent and cotangent bundle as opposed to the usual approach, where only the tangent spaces are relevant. In this thesis we will be interested in developing a formalism drinking from these ideas but for a toy model of eleven dimensional M-theory: three-form supergravity as introduced by Ovrut and Waldram.