  So far, flamelet theory has treated curvature as an independent parameter
requiring specific means for closure. In this work, it is shown how the
adoption of a two-dimensional orthogonal composition space allows obtaining
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 orthogonal coordinate system.
