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arXiv · 2210.15558

The spinor and Weierstrass representations of surfaces in space

Ivan Solonenko
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Abstract

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.

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Ivan Solonenko. 2022-10-27. The spinor and Weierstrass representations of surfaces in space. https://arxiv.org/abs/2210.15558

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