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Durham University

Department of Mathematical Sciences


Publication details for Professor Emeritus Wojtek Zakrzewski

A.M. Grundland & W.J. Zakrzewski (2003). CP^{N-1} Harmonic Maps and the Weierstrass Problem. Journal of Mathematical Physics 44(8): 3370-3382.

Author(s) from Durham


A Weierstrass-type system of equations corresponding to the CPN–1 harmonic maps is presented. The system constitutes a further generalization of our previous construction [J. Math. Phys. 44, 328 (2003)]. It consists of four first order equations for three complex functions which are shown to be equivalent to the CPN–1 harmonic maps. When the harmonic maps are holomorphic (or antiholomorphic) one of the functions vanishes and the system reduces to the previously given generalization of the Weierstrass problem. We also discuss a possible interpretation of our results and show that in our new case the induced metric is proportional to the total energy density of the map and not only to its holomorphic part, as was the case in the previous generalizations.