Higher genus minimal surfaces in S-3 and stable bundles
Higher genus minimal surfaces in S-3 and stable bundles
复制标题
S-3 和稳定丛中的更高属最小表面
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Sebastian Heller
中科院分区：
文献类型：
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作者：
Sebastian Heller
我们考虑与嵌入同伦的2属的紧极小曲面$ f_ mo S^3$。我们假设相关的全纯束是稳定的。我们用DPW方法证明了这些曲面可以由一个全局定义的亚纯连接族构造出来。亚纯连接的极点位于最多为2阶的黎曼曲面的weerstrass点上。为了证明DPW势的存在性，我们用自旋束S$的对偶$S^{-1}$用$P H^0（M;K^2）的关联元给出了自旋束S$的稳定扩展$0 o S^{-1} o v o S o 0$的刻画。我们还考虑了S^3中最小曲面上的全纯结构族。对于属$ggeq2$的曲面，连接的完整性是一般非阿贝尔的，因此全纯结构是一般稳定的。
We consider compact minimal surfaces $fcolon M o S^3$ of genus 2 which are homotopic to an embedding. We assume that the associated holomorphic bundle is stable. We prove that these surfaces can be constructed from a globally defined family of meromorphic connections by the DPW method. The poles of the meromorphic connections are at the Weierstrass points of the Riemann surface of order at most 2. For the existence proof of the DPW potential we give a characterization of stable extensions $0 o S^{-1} o V o S o 0$ of spin bundles $S$ by its dual $S^{-1}$ in terms of an associated element of $P H^0(M;K^2).$ We also consider the family of holomorphic structures associated to a minimal surface in $S^3.$ For surfaces of genus $ggeq2$ the holonomy of the connections is generically non-abelian and therefore the holomorphic structures are generically stable.
从 2 圆环到 4 球体的共形映射
DOI：
10.1515/crelle.2011.156
发表时间：
2012
期刊：
影响因子：
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作者：
Leschke;Pinkall
通讯作者：
Pinkall