Monopoles and harmonic maps

Recently Jarvis has proved a correspondence between SU(N) monopoles and rat ional maps of the Riemann sphere into flag manifolds. Furthermore, he has o utlined a construction to obtain the monopole fields from the rational map. In this paper we examine this construction in some detail and provide expl icit examples for spherically symmetric SU(N) monopoles with various symmet ry breakings. In particular we show how to obtain these monopoles from harm onic maps into complex projective spaces. The approach extends in a natural way to monopoles in hyperbolic space and we use it to construct new spheri cally symmetric SU(N) hyperbolic monopoles. (C) 1999 American Institute of Physics. [S0022-2488(99)03009-1].