摘要翻译:
R^4中区域上的正交复结构是可积的且与欧氏度量相容的复结构。由此得到一个共形不变的一阶偏微分方程组。本文证明了该方程组解的两个Liouville型唯一性定理,并利用这些定理给出了由Pontecorvo首先证明的紧局部共形平坦Hermitian曲面分类的另一个证明。在共形群的作用下,给出了CP^3中非退化二次曲面的一种分类。利用这种分类,我们证明了泛型二次曲面产生了定义在光滑嵌入R^4的未结实心环面的补上的正交复结构。
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英文标题:
《Orthogonal complex structures on domains in R^4》
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作者:
Simon Salamon and Jeff Viaclovsky
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Differential Geometry 微分几何
分类描述:Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形,接触,黎曼,伪黎曼和Finsler几何,相对论,规范理论,整体分析
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Analysis of PDEs 偏微分方程分析
分类描述:Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性,边界条件,线性和非线性算子,稳定性,孤子理论,可积偏微分方程,守恒律,定性动力学
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英文摘要:
An orthogonal complex structure on a domain in R^4 is a complex structure which is integrable and is compatible with the Euclidean metric. This gives rise to a first order system of partial differential equations which is conformally invariant. We prove two Liouville-type uniqueness theorems for solutions of this system, and use these to give an alternative proof of the classification of compact locally conformally flat Hermitian surfaces first proved by Pontecorvo. We also give a classification of non-degenerate quadrics in CP^3 under the action of the conformal group. Using this classification, we show that generic quadrics give rise to orthogonal complex structures defined on the complement of unknotted solid tori which are smoothly embedded in R^4.
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PDF链接:
https://arxiv.org/pdf/0704.3422