Canonical transformations for hyperkahler structures and hyperhamiltonian dynamics

TL;DR

This paper explores how canonical transformations extend to hyperkahler structures, highlighting differences from the symplectic case and examining hyperhamiltonian dynamics within this framework.

Contribution

It introduces and compares various notions of canonical transformations in hyperkahler geometry, clarifying their distinctions from symplectic transformations.

Findings

Different characterizations of hyperkahler transformations are not equivalent.

Hyperhamiltonian dynamics exhibit unique properties in the hyperkahler setting.

The paper clarifies the relationship between hyperkahler and canonical transformations.

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 raise to non-equivalent 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.