The axiom of hemi-slant 3-spheres in almost Hermitian geometry

The axiom of hemi-slant 3-spheres is introduced. It is proved that if an almost Hermitian manifold M with dimension 2m ? 6 satisfies this axiom for some slant angle ? ? (0,?/2); then M has pointwise constant type a if and only if M has pointwise constant anti-holomorphic sectional curvature a, and using this result some conditions for constancy of sectional curvature of a considered almost Hermitian manifold are given.