We exploit the Cartan-Kahler 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.

I.M. is partially supported by Contract DH/12/3/12.12.2017 and Contract 80-10-12/18.03.2020 with the Sofia University "St.Kl.Ohridski". J.S. is supported by the grant P201/12/G028 of the Grant Agency of the Czech Republic.