So far, flamelet theory has treated curvature as an independent parameter requiring spe- cific means for closure. In this work, it is shown how, when two-dimensional flames in physical space are considered, the adoption of an orthogonal flamelet coordinate system allows ob- taining formal mathematical relations between the flame curvatures and the gradients of the conditioning scalars (also called flamelet coordinates). With these, both curvatures become a flame response to the underlying flow, which conveniently allows removing them from the corresponding set of flamelet equations. While the demonstration is performed in the context of partially premixed flames, the approach is general and applicable to any two-dimensional orthogonal coordinate system.