Metric in the moduli of SU(2) monopoles from spectral curves and Gauss-Manin connection in disguise

Abstract: We show here that from the metric of the manifold $M<sup>0_2$ , i.e., the reduced moduli of SU(2) 2-monopoles in Yang-Mills-Higgs theory, one can recover the respective moduli of spectral curves using the method Gauss-Manin connection in disguise. This work is a step towards creating a inverse process of finding the metric of any $M<sup>0_k$ , from spectral curves. This is a thirty years old problem that we hope to shed some light in it.