On the modulus of level sets of conjugate submersions

We define and investigate pairs of (p,q)-conjugate submersions and - in particular - of (p,q)-conjugate functions. We show that conjugate submersions of the plane are p- and q-harmonic maps, respectively, if only 1p+1q=1. We prove that, in the case on an arbitrary Riemannian manifold, the reciprocity formula holds, i.e., the product of moduli of foliations defined by conjugate submersions is equal to one. Moreover, the product of the moduli of foliations that are merely locally given by conjugate submersions is not greater than one.