# Conformal Killing forms on nearly K\"ahler manifolds

## TL;DR

This paper classifies conformal Killing 3-forms on compact nearly K"ahler 6-manifolds, showing they are generated by the fundamental 2-form and its differential, with partial results on 2-forms.

## Contribution

It provides a complete classification of conformal Killing 3-forms on these manifolds and introduces an integrability condition for such forms.

## Key findings

- All conformal Killing 3-forms are linear combinations of dω and *dω.
- Non-existence of J-anti-invariant Killing 2-forms.
- Partial results on conformal Killing 2-forms.

## Abstract

We study conformal Killing forms on compact 6-dimensional nearly K\"ahler manifolds. Our main result concerns forms of degree 3. Here we give a classification showing that all conformal Killing 3-forms are linear combinations of $d \omega$ and its Hodge dual $* d\omega$ where $\omega$ is the fundamental 2-form of the nearly K\"ahler structure. The proof is based on a fundamental integrability condition for conformal Killing forms. We have partial results in the case of conformal Killing 2-forms. In particular we show the non-existence of J-anti-invariant Killing 2-forms.