CARTAN-TYPE CRITERIONS FOR CONSTANCY OF ALMOST HERMITIAN MANIFOLDS

Year 2013, Volume: 1 Issue: 2, 11 - 19, 01.12.2013

Hakan Mete Taştan

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

Keywords

Almost Hermitian manifold, Sectional curvature, Holomorphic sectional curvature, Constant type, Axiom of spheres

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