Anticonformal map ($\overline{f}\text{ is holomorphic with nonzero derivative}$)

An orientation-reversing local conformal map of planar domains. Equivalently, its complex conjugation is a holomorphic function with nonzero derivative. Complex conjugation $z\mapsto \bar{z}$ is the basic example. The metric pullback uses the modulus of its local scale factor, just as for an orientation-preserving conformal map.