  The variational problem for the functional
$F=\frac12\|\phi^*\omega\|_{L^2}^2$ is considered, where $\phi:(M,g)\to
(N,\omega)$ maps a Riemannian manifold to a symplectic manifold. This
functional arises in theoretical physics as the strong coupling limit of the
Faddeev-Hopf energy, and may be regarded as a symplectic analogue of the
Dirichlet energy familiar from harmonic map theory. The Hopf fibration
$\pi:S^3\to S^2$ is known to be a locally stable critical point of $F$. It is
proved here that $\pi$ in fact minimizes $F$ in its homotopy class and this
result is extended to the case where $S^3$ is given the metric of the Berger's
sphere. It is proved that if $\phi^*\omega$ is coclosed then $\phi$ is a
critical point of $F$ and minimizes $F$ in its homotopy class. If $M$ is a
compact Riemann surface, it is proved that every critical point of $F$ has
$\phi^*\omega$ coclosed. A family of holomorphic homogeneous projections into
Hermitian symmetric spaces is constructed and it is proved that these too
minimize $F$ in their homotopy class.
