The fundamental form of almost-quaternionic Hermitian manifolds

TL;DR

This paper proves that under certain conditions on the fundamental 4-form, an almost-quaternionic Hermitian manifold must be quaternionic-Kahler, revealing a key geometric characterization.

Contribution

It establishes a new characterization of quaternionic-Kahler manifolds via the conformal-Killing equation on the fundamental 4-form.

Findings

Fundamental 4-form satisfying conformal-Killing implies quaternionic-Kahler.

Results apply to manifolds of dimension at least eight.

Provides a geometric criterion for quaternionic-Kahler structure.

Abstract

We prove that if the fundamental 4-form of an almost-quaternionic Hermitian manifold (M, Q, g) of dimension at least eight satisfies the conformal-Killing equation, then (M, Q, g) is quaternionic-Kahler.