Canonical transformations for hyperkahler structures and hyperhamiltonian dynamics

Abstract

We discuss generalizations of the well known concept of canonical transformations for symplectic structures to the case of hyperkahler structures. Different characterizations, which are equivalent in the symplectic case, give rise to nonequivalent notions in the hyperkahler framework; we will thus distinguish between hyperkahler and canonical transformations. We also discuss the properties of hyperhamiltonian dynamics in this respect. © 2014 AIP Publishing LLC.