HP^3中的共形极小曲面的构造  

Construction of conformal minimal surfaces in HP^3

作　　者：张文娟 陈晓东 ZHANG Wenjuan;CHEN Xiaodong(School of Mathematical Sciences, University of Chinese Academy of Sciences, Beifing 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）》2018年第4期438-443,共6页Journal of University of Chinese Academy of Sciences

基　　金：国家自然科学基金(11331002;11471308)资助

摘　　要：通过扭映射π:CP^7→HP^3构造出HP^3中10族共形极小曲面的例子.根据Eells和Wood在1983年得到的结论,水平调和映射在淹没映射下的像仍然是调和的.首先给出CP^7中水平全纯曲面在局部下的一个分类定理.基于该分类定理以及Eells和Wood的结论,利用扭映射,构造出HP^3中的共形极小曲面.In this paper,we construct ten families of conformal minimal surfaces immersed into HP^3 by the twistor map π： CP^7→ HP^3. The construction is based on Eells and Wood＇s conclusion in 1983 that the projection of a horizontal harmonic map is also harmonic. Firstly, we give a characterization theorem for horizontal holomorphic surfaces in CP^7. By this theorem and Eells and Wood＇s conclusion,we get some conformal minimal surfaces immersed into HP^3 by the twisted map.

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]