Killing vector fields with twistor derivative

@article{Moroianu2005KillingVF,
  title={Killing vector fields with twistor derivative},
  author={Andrei Moroianu},
  journal={Journal of Differential Geometry},
  year={2005},
  volume={77},
  pages={149-167}
}
We describe all compact Riemannian manifolds carrying a Killing vector field whose covariant derivative (viewed as a 2-form) is a twistor form. 
The Dirac spectrum on manifolds with gradient conformal vector fields
Special Killing forms on Lorentzian spin manifolds
Killing 2-Forms in Dimension 4
Conformal Killing forms on $2$-step nilpotent Riemannian Lie groups

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