Hermitian manifolds of pointwise constant antiholomorphic sectional curvatures

TL;DR

This paper proves that in dimensions greater than four, Hermitian non-Kaehler manifolds with pointwise constant antiholomorphic sectional curvatures must have constant sectional curvatures, revealing a rigidity property.

Contribution

It establishes a rigidity result for Hermitian non-Kaehler manifolds, linking pointwise antiholomorphic curvature to global constant curvature in higher dimensions.

Findings

Hermitian non-Kaehler manifolds with pointwise constant antiholomorphic sectional curvatures are globally of constant curvature in dimensions >4.

The result extends curvature classification in Hermitian geometry.

Provides conditions under which local curvature properties imply global geometric structure.

Abstract

In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.