  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 the internal
geometry remains flat and uncorrected. For n=4, 6, Kahler manifolds with
SU(N)-holonomy can become corrected to SU(N)-structure, while preserving
supersymmetry, once corrections are included.
