Conformally parametrized surfaces associated with CP^(N-1) sigma models
Abstract
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.
Cite
@article{arxiv.0710.4366,
title = {Conformally parametrized surfaces associated with CP^(N-1) sigma models},
author = {A. M. Grundland and W. A. Hereman and I. Yurdusen},
journal= {arXiv preprint arXiv:0710.4366},
year = {2009}
}
Comments
32 pages