On the equivalence of quaternionic contact structures

TL;DR

This paper solves the equivalence problem for quaternionic contact structures using Cartan's method and parabolic geometry, providing a complete set of differential invariants and explicit geometric constructions.

Contribution

It offers the first complete solution to the local equivalence problem for quaternionic contact structures with explicit geometric and curvature data.

Findings

Constructed the Cartan geometry for quaternionic contact structures

Derived all curvature components explicitly

Provided a complete system of differential invariants

Abstract

Following the Cartans's original method of equivalence supported by methods of parabolic geometry, we provide a complete solution for the equivalence problem of quaternionic contact structures, that is, the problem of finding a complete system of differential invariants for two quaternionic contact manifolds to be locally diffeomorphic. This includes an explicit construction of the corresponding Cartan geometry and detailed information on all curvature components.