Minimal 2-spheres in ℂPn with constant Kähler angle

Abstract:

In 1988 the author and J. Bolton conjectured that a minimally immersed 2-sphere in ℂP ⁿ with constant Kähler angle θ≠ 0, π/2,π necessarily has constant curvature. In 1995 Li Zhen-qi showed that the simplest candidates for counterexamples must be linearly full in ℂP ¹⁰ with tan² (θ/2) = 3/4, and produced an explicit 3-parameter family of them. In the present paper it is shown that these counterexamples may be completely characterised using almost complex curves in the nearly Kähler S ⁶ and that the space of such counterexamples, modulo ambient isometries, is a 14-cell with a single point removed.