Almost K\"ahler manifolds whose antiholomorphic sectional curvature is pointwise constant

TL;DR

This paper proves that higher-dimensional almost K"ahler manifolds with pointwise constant antiholomorphic sectional curvature are actually complex space forms, revealing a strong geometric classification under these conditions.

Contribution

It establishes a classification result for almost K"ahler manifolds with pointwise constant antiholomorphic sectional curvature in dimensions ≥8.

Findings

Such manifolds are complex space forms.

Dimension ≥8 is critical for the classification.

The result links curvature conditions to complex space form structures.

Abstract

It is proved that if an almost K\"ahler manifold of dimension greater or equal to 8 is of pointwise constant antiholomorphic sectional curvature, then it is a complex space form.