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Surfaces associated with sigma models. (English) Zbl 1145.58303
Summary: 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 \(\mathbb CP^1\) sigma model, we obtain constant negative Gaussian curvature surfaces. As a consequence, this leads us to an explicit relation between the \(\mathbb CP^1\) sigma model and the sine-Gordon equation.

MSC:
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
53C43 Differential geometric aspects of harmonic maps
58E20 Harmonic maps, etc.
81T13 Yang-Mills and other gauge theories in quantum field theory
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