  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.
