On Bochner flat almost Kahler manifolds

TL;DR

This paper proves that certain high-dimensional almost Kähler manifolds with specific curvature conditions cannot exist, clarifying the geometric structure of these manifolds.

Contribution

It establishes a non-existence result for proper AK3-manifolds with vanishing Bochner tensor and constant scalar curvature in dimensions six and higher.

Findings

No proper AK3-manifolds with the specified curvature conditions exist in dimensions 6 and above.

The result constrains the geometric possibilities for almost Kähler manifolds under these curvature constraints.

Abstract

The main purpose of this article is to prove that there exist no proper $AK_3$-manifold of dimension $2n\ge 6$ with vanishing Tricerri-Vanhecke Bochner curvature tensor and constant scalar curvature.