A characterization of quaternionic projective space by the conformal-Killing equation

TL;DR

This paper proves that certain quaternionic-Kähler manifolds with specific conformal-Killing 2-forms are isomorphic to quaternionic projective space, providing a characterization of these spaces based on conformal geometry properties.

Contribution

It establishes a new characterization of quaternionic projective space via the existence of non-Killing conformal-Killing 2-forms on compact quaternionic-Kähler manifolds.

Findings

Quaternionic projective space characterized by conformal-Killing 2-forms

Compact quaternionic-Kähler manifolds with such forms are isomorphic to quaternionic projective space

Provides a geometric criterion for identifying quaternionic projective space

Abstract

We prove that a compact quaternionic-K\"{a}hler manifold of dimension $4n\geq 8$ admitting a conformal-Killing 2-form which is not Killing, is isomorphic to the quaternionic projective space, with its standard quaternionic-K\"{a}hler structure.