Conformally parametrized surfaces associated with CP^(N-1) sigma models

Details Conformally parametrized surfaces associated with CP^(N-1) sigma models Conformally parametrized surfaces associated with CP^(N-1) sigma models

2007-10-24

arxiv.org/abs/0710.4366v1

J. Phys. A: Math. Theor. 41 (2008) 065204

Mathematics

Differential Geometry

32 pages

Scientific paper

10.1088/1751-8113/41/6/065204

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.

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