  Two-dimensional conformally parametrized surfaces immersed in the su(N)
algebra are investigated. The focus is on surfaces parametrized by solutions of
the equations for the CP^(N-1) sigma model. The Lie-point symmetries of the
CP^(N-1) model are computed for arbitrary N. The Weierstrass formula for
immersion is determined and an explicit formula for a moving frame on a surface
is constructed. This allows us to determine the structural equations and
geometrical properties of surfaces in R^(N^2-1). The fundamental forms,
Gaussian and mean curvatures, Willmore functional and topological charge of
surfaces are given explicitly in terms of any holomorphic solution of the CP^2
model. The approach is illustrated through several examples, including surfaces
immersed in low-dimensional su(N) algebras.
