Minimal surfaces with constant Kähler angle in complex projective spaces

Abstract

Let ψ : S 2 → C P n \psi :{S^2} \to C{P^n} be an isometric minimal immersion of the Riemann sphere S 2 {S^2} into C P n C{P^n} with constant Kähler angle θ \theta . In this paper, we prove that Bolton et al.’s conjecture holds if θ \theta is not too close to π 2 \frac {\pi }{2} , that is, ψ \psi is ± \pm holomorphic or belongs to the Veronese sequence if | cos ⁡ θ | ≥ 1 5 |\cos \theta | \geq \frac {1}{5} .