T-duality and non-geometric solutions from double geometry

Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles in extended geometry. A proposal for solving this problem is given in the framework of double field theory. It is based on a clearly defined extension of the definition of gauge symmetry by isometries of an underlying pseudo-Riemannian manifold. The ensuing relation between transformations of coordinates and fields, which is now derived from first principles, differs from earlier proposals.