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Acta Mathematica Scientia

, Volume 39, Issue 4, pp 1065–1080 | Cite as

Equivariant Minimal Immersions from S3 into ℂP3

  • Zejun Hu (胡泽军)Email author
  • Jiabin Yin (尹佳斌)Email author
Article
  • 14 Downloads

Abstract

Associated with an immersion φ : S3 → ℂP3, we can define a canonical bundle endomorphism F : TS3TS3 by the pull back of the Kahler 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 

2010 MR Subject Classification

53C24 53C42 53C55 

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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouChina

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