String corrected spacetimes and SU(N) -structure manifolds

Using an effective field theory approach and the language of SU(N) -structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that internal geometry remains flat and uncorrected. For n=4,6 , Kähler manifolds with SU(N) -holonomy can become corrected to SU(N) -structure, while preserving supersymmetry, once corrections are included