On the axiom of planes and the axiom of spheres in the almost Hermitian geometry

Abstract

Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic planes or the axiom of antiholomorphic spheres is a real or a complex space form.

MR 84b:53057; 6 pages

Cited by in corpus (3)

• Curvature properties and isotropic planes of Riemannian and almost Hermitian manifolds of indefinite metrics
• The axiom of coholomorphic (2n+1)-spheres in the almost Hermitian geometry
• The axiom of θ-holomorphic 2-planes in the almost Hermitian geometry