Minimizing tangent maps into complex projective space

Abstract: We classify all nonconstant smooth harmonic maps $\mathbb{S}^2\to \mathbb{CP}<sup>n$ and $\mathbb{S}^3\to \mathbb{CP}<sup>n$ whose 0-homogeneous extensions are minimizing: they are, respectively, isometric embeddings or holomorphic isometric embeddings composed with a Hopf map.