Helicity is the only integral invariant of volume-preserving   transformations
  We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional $\mathcal I$ defined on exact divergence-free vector fields of class $C^1$ on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that $\mathcal I$ is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity. 
Alberto Enciso, Daniel Peralta-Salas, Francisco Torres de Lizaur
math.DS math-ph math.DG math.MP