Point vortex dynamics on Kähler twistor spaces

Abstract

In this paper, we provide tools to study the dynamics of point vortex dynamics on CPn and the flag manifold F1,2(C3). These are the only Kähler twistor spaces arising from four-manifolds. We give an explicit expression for Green’s function on CPn, which enables us to determine the Hamiltonian H and the equations of motions for the point vortex problem on CPn. Moreover, we determine the momentum map μ:F1,2(C3)→su*(3) on the flag manifold.