Almost Hermitian Manifolds with Vanishing Bochner Curvature Tensor

TL;DR

This paper proves that almost Hermitian manifolds with vanishing Bochner curvature tensor are flat near points where they are not Kaehlerian, revealing a local flatness property under certain curvature conditions.

Contribution

It establishes a new local flatness result for almost Hermitian manifolds with vanishing Bochner curvature tensor that are not Kaehlerian at a point.

Findings

Vanishing Bochner curvature tensor implies local flatness near non-Kaehlerian points.

The result applies to manifolds of dimension greater than 4.

Provides conditions under which almost Hermitian manifolds are flat.

Abstract

It is proved that if an almost Hermitian manifold of dimension greater than 4 has vanishing (classical) Bochner curvature tensor and is not Kaehlerian at a point, then it is flat in a neighbourhood of this point.