On almost complex surfaces of the nearly Kaehler 6-sphere II

Abstract

Let M be a 2-dimensional almost complex submanifold with Gauss curvature K in the nearly Kaehler unit 6-sphere S⁶(1). Then, in case K is constant, either K=1, K=1/6 or K=0 [S]. In [D-0-V-V], we proved that for compact M, if 1/6{≤}K{≤}1, then either K=1 or K=1/6. In the present paper we prove that for compact M, if 0{≤}K{≤}1/6, then either K=0 or K=1/6.