Equivariant CR minimal immersions from $S^3$ into $\mathbb{C}{P}^n$

Abstract

The equivariant CR minimal immersions from the round $3$-sphere $S^3$ into the complex projective space $\mathbb{C}{P}^n$ 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 $S^3=\mathrm{SU}(2)$ endowed with a left-invariant metric can be expressed in terms of the structure constants of the Lie algebra $\mathfrak{su}(2)$, we establish an extended classification theorem for equivariant CR minimal immersions from the $3$-sphere $S^3$ into $\mathbb{C}{P}^n$ without the assumption of constant sectional curvatures.

arXiv comment23 pages;This article has been accepted for publication in Annals of Global Analysis and Geometry

References in corpus (1)

• The almost sure limits of the minimal position and the additive martingale in a branching random walk

Cited by in corpus (1)

• Special Lagrangians in nearly Kähler ${\mathbb{CP}}^3$