Schur's Theorem for Almost Hermitian Manifolds

TL;DR

This paper proves a version of Schur's theorem for almost Hermitian manifolds, showing that pointwise constant antiholomorphic sectional curvature implies a global constant curvature in dimensions six and higher.

Contribution

It extends Schur's theorem to almost Hermitian manifolds, establishing a global curvature constancy under specific conditions.

Findings

Pointwise constant antiholomorphic sectional curvature implies global constancy.

The theorem applies to connected almost Hermitian manifolds of dimension ≥ 6.

Curvature is shown to be a global constant under the given conditions.

Abstract

The Schur's theorem of antiholomorphic type is proved for arbitrary almost Hermitian manifolds, namely: If a connected almost Hermitian manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then this curvature is a global constant.