Invariant operators on manifolds with almost Hermitian symmetric structures, II. Normal Cartan connections

Abstract

In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of this theory to the construction of natural operators. In this part we will extend the results of \cite{Ochiai, 70} on the existence and the uniqueness of the so called normal Cartan connections on manifolds with almost Hermitian symmetric structures to first order structures which do not admit a torsion free linear connection. Moreover, for each of these structures we obtain explicit (universal) formulae for these canonical connections in the terms of the curvatures of the underlying linear connections.