  In this paper, the Weierstrass technique for harmonic maps S^2 -> CP^(N-1) is
employed in order to obtain surfaces immersed in multidimensional Euclidean
spaces. It is shown that if the CP^(N-1) model equations are defined on the
sphere S^2 and the associated action functional of this model is finite, then
the generalized Weierstrass formula for immersion describes conformally
parametrized surfaces in the su(N) algebra. In particular, for any holomorphic
or antiholomorphic solution of this model the associated surface can be
expressed in terms of an orthogonal projector of rank (N-1). The implementation
of this method is presented for two-dimensional conformally parametrized
surfaces immersed in the su(3) algebra. The usefulness of the proposed approach
is illustrated with examples, including the dilation-invariant meron-type
solutions and the Veronese solutions for the CP^2 model. Depending on the
location of the critical points (zeros and poles) of the first fundamental form
associated with the meron solution, it is shown that the associated surfaces
are semi-infinite cylinders. It is also demonstrated that surfaces related to
holomorphic and mixed Veronese solutions are immersed in R^8 and R^3,
respectively.
