Surfaces associated with sigma models and the sine-Gordon equation
Differential Geometry
2007-05-23 v1
Abstract
We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional surfaces immersed in the su(N) algebra. In the special case of the CP^1 sigma model we obtain constant negative Gaussian curvature surfaces. As a consequence, this leads us to an explicit relation between the CP^1 sigma model and the sine-Gordon equation.
Cite
@article{arxiv.math/0601302,
title = {Surfaces associated with sigma models and the sine-Gordon equation},
author = {A. M. Grundland and L. Snobl},
journal= {arXiv preprint arXiv:math/0601302},
year = {2007}
}
Comments
36 pages, 10 figures