GEOMETRY OF T-DUALITY

A ''reduced'' differential geometry adapted to the presence of abelian isometries is constructed. Classical T-duality diagonalizes in this s etting, allowing us to get conveniently the transformation of the rele vant geometrical objects such as connections, pullbacks and generalize d curvatures. Moreover we can induce privileged maps from the viewpoin t of covariant derivatives in the target space and in the world-sheet generalizing previous results, at the same time that we can correct co nnections and curvatures covariantly in order to have a proper transfo rmation under T-duality. (C) 1998 Elsevier Science B.V.