Sur le théorème de F. Schur pour une variété presque hermitienne

Abstract

Let M be an almost Hermitian manifold of dimension greater or equal to 6. The following theorems are proved: Theorem 1. If M is of pointwise constant θ-holomorphic sectional curvature for a number θ in (0,π/2) then M is of constant sectional curvature or a Kähler manifold of constant holomorphic sectional curvature. Theorem 2. If M is of pointwise constant antiholomorphic sectional curvature and M is an RK-manifold (or AH3-manifold), then M is of constant antiholomorphic sectional curvature.

3 pages, MR 84c:53022

References in corpus (1)

• Nearly Kähler manifolds of constant antiholomorphic sectional curvature

Cited by in corpus (1)

• Almost Kähler manifolds whose antiholomorphic sectional curvature is pointwise constant