SU(N) skyrmions and harmonic maps

Harmonic maps from S-2 to CPN-1 are introduced to construct low-energy conf igurations of the SU(N) Skyrme model. We show that one of such maps gives a n exact, topologically trivial, solution of the SU(3) model. We study vario us properties of these maps and show that, in general, their energies are o nly a little higher than the energies of the corresponding SU(2) embeddings . Moreover, we show that the baryon and energy densities of the SU(3) confi gurations with baryon number B=3-6 are more symmetrical than their SU(2) an alogs, thus suggesting that there exist solutions of the model with these s ymmetries. We also show that any SU(2) solution embedded into the SU(4) Sky rme model becomes a topologically trivial solution of this model. (C) 1999 American Institute of Physics. [S0022-2488(99)02712-7].