Conformally parametrized surfaces associated with CPN−1 sigma models

Two-dimensional 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 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.