I will describe work in progress, joint with Dmitri Panov. A definite connection is an \(SO(3)\)-connection over a \(4\)-manifold, whose curvature is non-zero on every tangent \(2\)-plane. Given such a connection, the associated \(2\)-sphere bundle is naturally a symplectic manifold. In this talk I will be interested in definite connections invariant under a circle action, in which case the corresponding symplectic six-manifold is “Fano". I will explain how we hope to classify them, the only possibilities should be connections over \(S^4\) or \(\operatorname{CP}^2\) giving Fanos \(\operatorname{CP}^3\) and the complete flag on \(C^3\) respectively.