  We show how the tangent bundle decomposition generated by a system of
ordinary differential equations may be generalized to the case of a system of
second order PDEs `of connection type'. Whereas for ODEs the decomposition is
intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold
of independent variables, together with a transverse local vector field. The
resulting decomposition provides several natural curvature operators. The
harmonic map equation is examined, and in this case both the 1-form and the
vector field arise naturally.
