Volume 37 • Number 2 • 2014   • The Axiom of Hemi-Slant 3-Spheres in Almost Hermitian Geometry Hakan Mete Taştan Abstract. The axiom of hemi-slant 3-spheres is introduced. It is proved that if an almost Hermitian manifold $M$ with dimension $2m\geq6$ satisfies this axiom for some slant angle $θ∈(0,π/2),$ then $M$ has pointwise constant type $\alpha$ if and only if $M$ has pointwise constant anti-holomorphic sectional curvature $\alpha$, and using this result some conditions for constancy of sectional curvature of a considered almost Hermitian manifold are given. 2010 Mathematics Subject Classification: Primary 53B35, 53B25; Secondary 53C40 Full text: PDF