Nahm's equations and hyperkähler geometry (Q1315015)

A 12-dimensional moduli space \(M\) of solutions to Nahm's equations is introduced here. It is shown that \(M\) has a hyperkähler structure and is acted on isometrically by \(U(2)\) and \(\text{Spin}(3)\). The hyperkähler quotient of \(M\) by the centre of \(U(2)\) is a 8-dimensional hyperkähler manifold whose totally geodesic submanifold which represents axisymmetric solutions to the Nahm's equations is studied. Finally, a family of gravitational instantons is shown to arise as a deformation of the Atiyah-Hitchin manifold.