  In some higher dimensional nonlinear field theories integrable subsectors
with infinitely many conservation laws have been identified by imposing
additional integrability conditions. Originally, the complex eikonal equation
was chosen as integrability condition, but recently further generalizations
have been proposed. Here we show how these new integrability conditions may be
derived from the geometry of the target space and, more precisely, from the
Noether currents related to a certain class of target space transformations.
