| HP3中共形极小曲面的几何 |
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| 作者姓名： | 高紫娟 焦晓祥 |
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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（11871450）资助 |
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| 摘 要： | 通过扭映射π：CP7→HP3构造出HP3中曲率为4/7，4/19，4/27的6个共形极小二维球面的例子.由于扭映射π：CP2n+1→HPn给出了CP2n+1的水平极小曲面与HPn中极小曲面的一个自然等同，利用Bolton等得出的在CPn中常曲率共形极小二维球面的结论，根据CHEN Xiaodong和JIAO Xiaoxiang给出的HPn中常曲率共形极小二维球面的一般方法，构造出HPn中的共形极小曲面的例子.
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| 关 键 词： | 四元数射影空间 共形极小曲面 扭映射 |
| 收稿时间： | 2017-10-26 |
| 修稿时间： | 2017-12-25 |
The geometry of conformal minimal surfaces in HP3 |
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| Authors: | GAO Zijuan JIAO Xiaoxiang |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | In this work, we construct six examples of conformal minimal two-spheres surfaces with constant curvatures of 4/7, 4/19, and 4/27 by the twistor map π:CP7→HP3. By the twistor map, we know that the horizontal minimal surfaces in CP2n+1 are equivalent to the minimal surfaces in HPn, and many conclusions about conformal minimal two-spheres with constant curvatures in CPn have been given. Based on Bolton's conclusion and Chen's general method to construct conformal minimal two-spheres, we get some conformal minimal two-sphere surfaces in HP3. |
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| Keywords: | quaternionic projective space conformal minimal surface twistor map |
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