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数学与物理学

S2到HP4的共形极小浸入

  • 焦晓祥 ,
  • 崔洪斌
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  • 中国科学院大学数学科学学院, 北京 100049

收稿日期: 2019-04-03

  修回日期: 2019-05-06

  网络出版日期: 2020-11-15

基金资助

Supported by the NSFC(11871450)

Conformal minimal immersions of S2 into HP4

  • JIAO Xiaoxiang ,
  • CUI Hongbin
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2019-04-03

  Revised date: 2019-05-06

  Online published: 2020-11-15

Supported by

Supported by the NSFC(11871450)

摘要

本工作是Chen和Jiao工作的推广。他们考虑在四元数射影空间中如何具体构造常曲率共形极小二球,关键点是从CP2n+1里的Veronese序列找到一些相关的水平浸入,然后关于扭映射π:CP2n+1→ HPn做投影就得到HPn的常曲率共形极小二球。Chen和Jiao计算了n=2的情况,本工作处理n=4的情况和一个相关的几何现象。

本文引用格式

焦晓祥 , 崔洪斌 . S2到HP4的共形极小浸入[J]. 中国科学院大学学报, 2020 , 37(6) : 721 -727 . DOI: 10.7523/j.issn.2095-6134.2020.06.001

Abstract

This work is a generalization of Chen and Jiao's work, where they considered the question of explicit construction of some conformal minimal two-spheres of constant curvature in quaternionic projective space. The crucial point was to find some horizontal immersions derived from Veronese sequence in CP2n+1, which was projected into constant curvature conformal minimal two-spheres by twistor map π:CP2n+1→HPn. They calculated the case n=2. In this work, we deal with the case n=4 and a related geometry phenomenon.

参考文献

[1] Calabi E. Minimal immersions of surfaces in Euclidean spheres[J]. J Differ Geom, 1967, 1:111-125.
[2] Bolton J, Jensen G R, Rigoli M, et al. On conformal minimal immersion of S2 into CPn[J]. Math Ann, 1988, 279:599-620.
[3] Eells J, Wood J C. Harmonic maps from surfaces to complex projective spaces[J]. Adv Math, 1983, 49:217-263.
[4] Bryant R L. Conformal and minimal immersions of compact surfaces into the 4-sphere[J]. J Differ Geom, 1982, 17:455-473.
[5] Aithal A R. Harmonic maps from S2 to HP2[J]. Osaka J Math, 1986, 23:255-270.
[6] Bahy-El-Dien A, Wood J C. The explicit construction of all harmonic two-spheres in quaternionic projective spaces[J]. Proc Lond Math Soc, 1991, 62:202-224.
[7] He L, Jiao X X. Classification of conformal minimal immersions of constant curvature from S2 to HP2[J]. Math Ann, 2014, 359:663-694.
[8] He L, Jiao X X. On conformal minimal immersions of S2 in[XCH.TIF,JZ]Pn with parallel second fundamental form[J]. Annali di Matematica Pura ed Applicata, 2015, 194:1301-1317.
[9] He L, Jiao X X. On conformal minimal immersions of constant curvature from S2 to HPn[J]. Mathematische Zeitschrift, 2015, 280(3/4):1-21.
[10] Chen X D, Jiao X X. Conformal minimal surfaces immersed into HPn[J]. Annali di Matematica Pura ed Applicata, 2017, 196:2063-2076.
[11] Yang K. Complete and compact minimal surfaces[C]. Dordrecht:Kluwer Academic Publishers, 1989:66-67.
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