论文标题
太空中表面的旋转器和Weierstrass表示
The spinor and Weierstrass representations of surfaces in space
论文作者
论文摘要
在本文中，在沙利文，库斯纳和施密特之后，我们研究了三维欧几里得空间中黎曼表面的共形浸入。关于从表面的切线束到二维球体的cotangent束等特殊捆绑图的浸入，我们将最小表面的经典Weierstrass代表推广到了任意保质浸入的情况下。我们研究了这种浸入如何与一对旋转器一起在表面上产生旋转结构，以及如何通过这些纺纱剂研究浸入本身。
In this paper, following Sullivan, Kusner, and Schmitt, we study conformal immersions of Riemann surfaces into the three-dimensional Euclidean space. Regarding such immersions as special bundle maps from the tangent bundle of the surface to the cotangent bundle of the 2-dimensional sphere, we generalize the classical Weierstrass representation of minimal surfaces to the case of arbitrary conformal immersions. We study how such an immersion gives rise to a spin structure on the surface together with a pair of spinors and how the immersion itself can be studied by means of these spinors.
