Conformal Killing-Yano 2-forms

Riemannian manifolds carrying 2-forms satisfying the Killing-Yano equation and the conformal Killing-Yano equation are natural generalizations of nearly Kähler and Sasakian manifolds. In this article we exhibit new solutions of these equations. We also provide obstructions for their existence on Lie groups, and reduce the study of conformal Killing-Yano 2-forms to a particular class of non degenerate Killing-Yano 2-forms.