EQUIVARIANT MINIMAL IMMERSIONS FROM S3 INTO CP3

doi:10.1007/s10473-019-0411-3

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 1065-1080.doi: 10.1007/s10473-019-0411-3

EQUIVARIANT MINIMAL IMMERSIONS FROM S³ INTO CP³

胡泽君, 尹佳斌

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

收稿日期:2018-01-12 修回日期:2018-06-26 出版日期:2019-08-25 发布日期:2019-09-12
作者简介:Zejun HU,E-mail:huzj@zzu.edu.cn;Jiabin YIN,E-mail:welcomeyjb@163.com
基金资助:
The authors were supported by NSF of China (11771404).

EQUIVARIANT MINIMAL IMMERSIONS FROM S³ INTO CP³

Zejun HU, Jiabin YIN

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

Received:2018-01-12 Revised:2018-06-26 Online:2019-08-25 Published:2019-09-12
Supported by:
The authors were supported by NSF of China (11771404).

摘要/Abstract

摘要： Associated with an immersion φ:S³ → CP³, we can define a canonical bundle endomorphism F:TS³→TS³ by the pull back of the Kähler form of CP³. In this article, related to F we study equivariant minimal immersions from S³ into CP³ under the additional condition (▽_XF)X=0 for all X ∈ ker (F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant non-minimal immersion φ:S³ → CP³ satisfying (▽_XF)X=0 for all X ∈ ker (F), which is neither Lagrangian nor of CR type.

关键词: Complex projective space, equivariant, minimal, 3-sphere

Abstract: Associated with an immersion φ:S³ → CP³, we can define a canonical bundle endomorphism F:TS³→TS³ by the pull back of the Kähler form of CP³. In this article, related to F we study equivariant minimal immersions from S³ into CP³ under the additional condition (▽_XF)X=0 for all X ∈ ker (F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant non-minimal immersion φ:S³ → CP³ satisfying (▽_XF)X=0 for all X ∈ ker (F), which is neither Lagrangian nor of CR type.

Key words: Complex projective space, equivariant, minimal, 3-sphere

中图分类号:

53C24

胡泽君, 尹佳斌. EQUIVARIANT MINIMAL IMMERSIONS FROM S³ INTO CP³[J]. 数学物理学报(英文版), 2019, 39(4): 1065-1080.

Zejun HU, Jiabin YIN. EQUIVARIANT MINIMAL IMMERSIONS FROM S³ INTO CP³[J]. Acta mathematica scientia,Series B, 2019, 39(4): 1065-1080.

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EQUIVARIANT MINIMAL IMMERSIONS FROM S³ INTO CP³

EQUIVARIANT MINIMAL IMMERSIONS FROM S³ INTO CP³

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