Equivariant Minimal Immersions from S3 into ℂP3
Associated with an immersion φ : S3 → ℂP3, we can define a canonical bundle endomorphism F : TS3 → TS3 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 wordsComplex projective space equivariant minimal 3-sphere
2010 MR Subject Classification53C24 53C42 53C55
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