HP^3中共形极小曲面的几何  

The geometry of conformal minimal surfaces in HP^3

作　　者：高紫娟 焦晓祥 GAO Zijuan;JIAO Xiaoxiang(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2019年第3期299-310,共12页Journal of University of Chinese Academy of Sciences

基　　金：国家自然科学基金(11871450)资助

摘　　要：通过扭映射π:CP^7→HP^3构造出HP^3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:CP^(2n+1)→HP^n给出了CP^(2n+1)的水平极小曲面与HP^n中极小曲面的一个自然等同,利用Bolton等得出的在CP^n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HP^n中常曲率共形极小二维球面的一般方法,构造出HP^n中的共形极小曲面的例子.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.

关 键 词：四元数射影空间 共形极小曲面 扭映射 

分 类 号：O186.1[理学—数学]