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In this paper we construct a Hitchin connection in a setting, whichsignificantly generalizes the setting covered by the first author previously,which in turn was a generalisation of the moduli space case covered by Hitchinin his original work on the Hitchin connection. In fact, our constructionprovides a Hitchin connection, which is a partial connection on the space ofall compatible complex structures on an arbitrary, but fixed prequantizablesymplectic manifold, which satisfies a certain Fano type condition. Thesubspace of the tangent space to the space of compatible complex structures onwhich the constructed Hitchin connection is defined, is in fact of finiteco-dimension, if the symplectic manifold is compact. In a number of examples,including flat symplectic space, symplectic tori and moduli spaces of flatconnections for a compact Lie group, we prove that our Hitchin connection isdefined in a neighbourhood of the natural families of complex structurescompatible with the given symplectic form, which these spaces admits.

A Hitchin Connection for a large class of families of K\"ahler Structures