  Recent papers have established the relationship between projective superspace
and a complexified version of harmonic superspace. We extend this construction
to the case of general nonlinear sigma models in both frameworks. Using an
analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian
structure of the harmonic action and the symplectic structure of the projective
action naturally arise from a single unifying action on a complexified version
of harmonic superspace. This links the harmonic and projective descriptions of
hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson,
we show how to derive the projective superspace solutions from the harmonic
superspace solutions.
