Minimal 2-spheres in a complex projective space

In this paper conformal minimal 2-spheres immersed in a complex projective space are studied by applying Lie theory and moving frames. We give differential equations of Kähler angle and square length of the second fundamental form. By applying these differential equations we give characteristics of conformal minimal 2-spheres of constant Kähler angle and obtain pinching theorems for curvature. We also discuss conformal minimal 2-spheres of constant normal curvature and prove that there does not exist any linearly full minimal 2-sphere immersed in a complex projective space CPnCPn (n>2n>2) with non-positive constant normal curvature. We also prove that a linearly full minimal 2-sphere immersed in a complex projective space CPnCPn (n>2n>2) with constant normal curvature and constant Kähler angle is of constant curvature.