It is known that a contact Riemannian manifold carries a generalized Fefferman metric on a circle bundle over the manifold. We compute the curvature of the metric explicitly in terms of a modified Tanno connection on the underlying manifold. In particular, we show that the scalar curvature descends to the pseudohermitian scalar curvature multiplied by a certain constant. This is an answer to a problem considered by Blair-Dragomir.
"On the curvature of the Fefferman metric of contact Riemannian manifolds." Tohoku Math. J. (2) 71 (3) 425 - 436, 2019. https://doi.org/10.2748/tmj/1568772179