| 非零Gauss曲率Bonnet曲面的存在性及其相关性质 |
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| 作者姓名： | 王珂 吴英毅 |
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| 作者单位： | 中国科学院大学数学科学学院, 北京 100049 |
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| 基金项目： | 国家自然科学基金（11471308）资助 |
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| 摘 要： | 研究关于Bonnet曲面的两个问题。第一，通过研究Bonnet曲面的平均曲率所满足的常微分方程证明Gauss曲率不恒为零的Bonnet曲面一定存在。第二，证明若两张Bonnet曲面之间存在一个保主曲率且保定向的共形映射，则有以下两种情形：如果两曲面的Gauss曲率零点孤立，则该共形映射必为等距；如果两曲面的Gauss曲率恒为零，则该共形映射为相似变换。
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| 关 键 词： | Bonnet曲面 W-曲面 共形映射 相似变换 |
| 收稿时间： | 2018-09-12 |
| 修稿时间： | 2018-12-30 |
Existence and related properties of non-zero Gaussian curvature Bonnet surfaces |
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| Authors: | WANG Ke WU Yingyi |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | We study two problems about Bonnet surfaces. First, we prove that the Bonnet surface whose Gaussian curvature is not identically zero must exist by studying the ordinary differential equation which the mean curvature of the Bonnet surface satisfies. Secondly, we prove that if there exists a conformal map which preserves the principal curvatures and the orientation between two Bonnet surfaces, then there are two cases as follows:1) If the zero points of the Gaussian curvature of the two surfaces are isolated, then the conformal map must be an isometry. 2) If the Gaussian curvature of the two surfaces is identically zero, then the conformal map is a similarity transformation. |
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| Keywords: | Bonnet surface W-surface conformal map similarity transformation |
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