Almost K\"ahler manifolds of constant antiholomorphic sectional curvature

TL;DR

This paper proves that higher-dimensional almost Kähler manifolds with pointwise constant antiholomorphic sectional curvature are either of constant negative sectional curvature or are Kähler with constant holomorphic sectional curvature.

Contribution

It establishes a classification result for AK2-manifolds of dimension ≥6 with pointwise constant antiholomorphic sectional curvature.

Findings

AK2-manifolds of dimension ≥6 with this property are either of constant negative sectional curvature or Kähler with constant holomorphic sectional curvature.

The result extends understanding of curvature conditions in almost Kähler geometry.

It provides a dichotomy for the geometric structure of such manifolds.

Abstract

It is proved that if an AK2-manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then it is a 6-dimensional manifold of constant negative sectional curvature or a K\"ahler manifold of constant holomorphic sectional curvature.