CP^{N-1} Harmonic Maps and the Weierstrass Problem

Grundland, A.M.; Zakrzewski, W.J.

doi:10.1063/1.1586791

CP^{N-1} Harmonic Maps and the Weierstrass Problem

Grundland, A.M.; Zakrzewski, W.J.

Authors

A.M. Grundland

W.J. Zakrzewski

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.

Citation

Grundland, A., & Zakrzewski, W. (2003). CP^{N-1} Harmonic Maps and the Weierstrass Problem. Journal of Mathematical Physics, 44(8), 3370-3382. https://doi.org/10.1063/1.1586791

Journal Article Type	Article
Publication Date	Aug 1, 2003
Deposit Date	Apr 25, 2007
Publicly Available Date	Apr 26, 2011
Journal	Journal of Mathematical Physics
Print ISSN	0022-2488
Electronic ISSN	1089-7658
Publisher	American Institute of Physics
Peer Reviewed	Peer Reviewed
Volume	44
Issue	8
Pages	3370-3382
DOI	https://doi.org/10.1063/1.1586791

Files

Published Journal Article (111 Kb)
PDF

Copyright 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