CARTAN-TYPE CRITERIONS FOR CONSTANCY OF ALMOST HERMITIAN MANIFOLDS

Abstract

We studied the axiom of anti-invariant 2-spheres and the axiom ofco-holomorphic (2n + 1)-spheres. We proved that a nearly K¨ahlerian manifoldsatisfying the axiom of anti-invariant 2-spheres is a space of constant holomorphic sectional curvature. We also showed that an almost Hermitian manifoldM of dimension 2m ≥ 6 satisfying the axiom of co-holomorphic (2n+1)-spheresfor some n, where (1 ≤ n ≤ m − 1), the manifold M has pointwise constanttype α if and only if M has pointwise constant anti-holomorphic sectionalcurvature α