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.
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