从CP ^（N-1）sigma模型获得的表面
Surfaces obtained from CP^(N-1) sigma models
摘要：
本文利用调和映射S^2 -> CP^（N-1）的Weierstrass技巧，得到了浸入多维欧几里得空间的曲面.证明了如果CP^（N-1）模型方程定义在球面S^2上，且该模型的作用泛函是有限的，则浸入的广义Weierstrass公式描述了su（N）代数中的共形参数化曲面.特别地，对于该模型的任何全纯或反全纯解，相关曲面可以用秩为（N-1）的正交投影表示。该方法的实现，提出了二维共形参数化曲面沉浸在su（3）代数。通过对CP^2模型的膨胀不变的meron型解和Veronese型解的计算，说明了该方法的有效性.依赖于与meron解决方案的第一基本型的临界点（零和极点）的位置，它示出，相关的表面是半无限的圆柱体。我们还证明了与全纯和混合Veronese解相关的曲面分别浸入R^8和R^3中。
英文摘要：
In this paper, the Weierstrass technique for harmonic maps S^2 -> CP^(N-1) is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the CP^(N-1) model equations are defined on the sphere S^2 and the associated action functional of this model is finite, then the generalized Weierstrass formula for immersion describes conformally parametrized surfaces in the su(N) algebra. In particular, for any holomorphic or antiholomorphic solution of this model the associated surface can be expressed in terms of an orthogonal projector of rank (N-1). The implementation of this method is presented for two-dimensional conformally parametrized surfaces immersed in the su(3) algebra. The usefulness of the proposed approach is illustrated with examples, including the dilation-invariant meron-type solutions and the Veronese solutions for the CP^2 model. Depending on the location of the critical points (zeros and poles) of the first fundamental form associated with the meron solution, it is shown that the associated surfaces are semi-infinite cylinders. It is also demonstrated that surfaces related to holomorphic and mixed Veronese solutions are immersed in R^8 and R^3, respectively.
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