For Kähler manifolds, we explicitly determine the solution to the conformal Killing form equation in middle degree. In particular, we complete the classification of conformal Killing forms on compact Kähler manifolds. We give the first examples of conformal Killing forms on Kähler manifolds not coming from Hamiltonian 2-forms. These are supported by Calabi-type manifolds over a Kähler Einstein base. In this setup, we also give structure results and examples for the closely related class of Hermitian Killing forms.
"Conformal Killing forms in Kähler geometry." Illinois J. Math. 66 (3) 349 - 384, September 2022. https://doi.org/10.1215/00192082-10088173