On the existence of local quaternionic contact geometries

Abstract

We exploit the Cartan-Kähler theory to prove the local existence of real analytic quaternionic contact structures for any prescribed values of the respective curvature functions and their covariant derivatives at a given point on a manifold. We show that, in a certain sense, the different real analytic quaternionic contact geometries in $4n+3$ dimensions depend, modulo diffeomorphisms, on $2n+2$ real analytic functions of $2n+3$ variables.

References in corpus (2)

• Notes on exterior differential systems
• Quaternionic contact hypersurfaces in hyper-Kähler manifolds