Surfaces associated with sigma models and the sine-Gordon equation

Details Surfaces associated with sigma models and the sine-Gordon equation Surfaces associated with sigma models and the sine-Gordon equation

2006-01-12

arxiv.org/abs/math/0601302v1

Mathematics

Differential Geometry

36 pages, 10 figures

Scientific paper

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.

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