与CP ^（N-1）sigma模型相关的共形参数化曲面
Conformally parametrized surfaces associated with CP^(N-1) sigma models
摘要：
研究了浸入su（N）代数中的二维共形参数曲面。重点是表面参数化的解决方案的CP^（N-1）西格玛模型的方程。对于任意的N，计算CP^（N-1）模型的李点对称性。确定了浸入的Weierstrass公式，构造了曲面上活动标架的显式公式。这使我们能够确定R^（N^2-1）中曲面的结构方程和几何性质。利用CP^2模型的全纯解，给出了曲面的基本形式、高斯曲率和中曲率、Willmore泛函和拓扑荷。该方法通过几个例子，包括沉浸在低维su（N）代数的表面说明。
英文摘要：
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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