title: Helicity is the only integral invariant of volume-preserving transformations.
abstract: We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional 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 I is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.
authors: Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain aenciso@icmat.es dperalta@icmat.es fj.torres@icmat.es.
authors: Alberto
authors: A
authors: Enciso
authors: Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain aenciso@icmat.es dperalta@icmat.es fj.torres@icmat.es.
authors: Daniel
authors: D
authors: Peralta-Salas
authors: Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain aenciso@icmat.es dperalta@icmat.es fj.torres@icmat.es.
authors: Francisco Torres
authors: FT
authors: de Lizaur
keywords: helicity; integral invariant; volume-preserving transformation