An Einstein-Weyl structure is a natural generalization of an Einstein structure within the framework of conformal geometry. We are interested in considering an Einstein-Weyl structure on a CR manifold. A CR manifold has a conformal structure only on its hyperdistribution. In this paper, on a CR manifold we naturally define an Einstein-Weyl structure closely related to the conformal structure on the hyperdistribution.
"CR Einstein-Weyl structures." Tsukuba J. Math. 29 (2) 309 - 361, December 2005. https://doi.org/10.21099/tkbjm/1496164961