Generalized helicity and Beltrami fields

We propose covariant and non-abelian generalizations of the magnetic helicity and Beltrami equation. The gauge invariance, variational principle, conserved current, energy-momentum tensor and choice of boundary conditions elucidate the subject. In particular, we prove that any extremal of the Yang-Mills action functional 14∫ΩtrFμνFμνd4x subject to the local constraint εμναβtrFμνFαβ=0 satisfies the covariant non-abelian Beltrami equation.