  Helmholtz theorem states that, in ideal fluid, vortex lines move with the
fluid. Another Helmholtz theorem adds that strength of a vortex tube is
constant along the tube. The lines may be regarded as integral surfaces of a
1-dimensional integrable distribution (given by the vorticity 2-form). In
general setting of theory of integral invariants, due to Poincare and Cartan,
one can find $d$-dimensional integrable distribution whose integral surfaces
show both properties of vortex lines: they move with (abstract) fluid and, for
appropriate generalization of vortex tube, strength of the latter is constant
along the tube.
