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CP^{N-1} harmonic maps and the Weierstrass problem.

Grundland, A. M. and Zakrzewski, W. J. (2003) 'CP^{N-1} harmonic maps and the Weierstrass problem.', Journal of mathematical physics., 44 (8). pp. 3370-3382.

Abstract

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.

Item Type:Article
Full text:PDF - Published Version (109Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1063/1.1586791
Publisher statement:Copyright (2003) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. Grundland, A. M. and Zakrzewski, W. J. (2003) 'CP^{N-1} harmonic maps and the Weierstrass problem.', Journal of mathematical physics., 44 (8). pp. 3370-3382. and may be found at http://dx.doi.org/10.1063/1.1586791
Record Created:25 Apr 2007
Last Modified:26 Apr 2011 16:23

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