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Mathematics > Differential Geometry

arXiv:0710.4366 (math)
[Submitted on 24 Oct 2007]

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

Authors:A. M. Grundland, W. A. Hereman, I. Yurdusen
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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.
Comments: 32 pages
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:0710.4366 [math.DG]
  (or arXiv:0710.4366v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.4366
Journal reference: J. Phys. A: Math. Theor. 41 (2008) 065204
Related DOI: https://doi.org/10.1088/1751-8113/41/6/065204

Submission history

From: Ismet Yurdusen [view email]
[v1] Wed, 24 Oct 2007 01:11:41 UTC (26 KB)
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