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

## TL;DR

This paper extends the classification of equivariant CR minimal immersions from the 3-sphere into complex projective spaces by removing the constant curvature assumption, using Lie algebra structure constants.

## Contribution

It provides a broader classification theorem for equivariant CR minimal immersions without assuming constant sectional curvature.

## Key findings

- Extended classification of immersions without constant curvature assumption
- Utilized Lie algebra structure constants to analyze geometric properties
- Established conditions for equivariant CR minimal immersions

## Abstract

The equivariant CR minimal immersions from the round $3$-sphere $S^3$ into the complex projective space $\mathbb CP^n$ 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 $S^3={\rm SU}(2)$ 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 $\mathbb CP^n$ without the assumption of constant sectional curvatures.