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.