By Boris Khesin and others

We prove that the helicity is the only regular Casimir function for the coadjoint action of the volume-preserving diffeomorphism group *\text{SDiff}(M)* on smooth exact divergence-free vector fields on a closed three-dimensional manifold *M*. More precisely, any regular *C^1* functional defined on the space of *C^\infty* (more generally, *C^k*, *k\ge 4*)... Show more

March 12, 2020

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