Equivariant CR minimal immersions from $$S^3$$S3 into $$\mathbb CP^n$$CPn

Abstract

The equivariant CR minimal immersions from the round 3-sphere S 3 into the complex projective space CP n have been classified by the third author explicitly (J London Math Soc 68: 223-240, 2003). In this paper, by employing the equivariant condition which implies that the induced metric is left-invariant, and that all geometric properties of S 3 = SU(2) endowed with a left-invariant metric can be expressed in terms of the structure constants of the Lie algebra su(2), we establish an extended classification theorem for equivariant CR minimal immersions from the 3-sphere S 3 into CP n without the assumption of constant sectional curvatures.

Special Lagrangians in nearly Kähler CP3

“…CR immersion from S 3 to the Kähler CP n has been studied in [16]. The splitting T L = E ⊕ E ⊥ gives an ansatz for Lagrangians arising as a product X 2 × S 1 such that T X = E. Indeed, we will give such an example for θ ≡ 0 later.…”