On minimal surfaces with constant Kähler angle in \(\mathbb{C} P^ 3\) and \(\mathbb{C} P^ 4\) (Q1375719)

This paper gives a contribution to the study of minimal surfaces of complex projective space \(\mathbb{C} P^n\) with constant Kähler angle, assuming certain conditions on its harmonic sequences. Namely, the following is proved: Let \(M\) be a minimal surface with constant Kähler angle in \(\mathbb{C} P^n\). (i) If \(M\) is superconformal and \(n=3\), then \(M\) is totally real. (ii) If \(M\) is pseudo-holomorphic and \(n=4\), then \(M\) is either holomorphic, anti-holomorphic, totally real, or of constant curvature.