Some geometric aspects of maps

In this talk we introduce a Weierstrass-like system of equations corresponding to CP N -1 fields in two dimensions. Then using this representation we introduce a vector in R N 2-1 and treating this vector as the radius vector of a surface immersed in R N 2-1 we discuss to what extent the associated metric describes the geometry of the CP N -1 maps. We show that for the holomorphic maps - the correspondence is exact; while for the more general fields we have to go beyond the Weierstrass system and add extra terms. Received 1st August 2001 / Received in final form 18 October 2001 Published online 2 October 2002 RID="a" ID="a"Work done in collaboration with M. Grundland e-mail: w.j.zakrzewski@durham.ac.uk