We introduce the pseudo-Einstein structure on real hypersurfaces in a K\"ahlerian manifold, namely, the Ricci curvature tensor for the generalized Tanaka-Webster connection (restricted) on the Levi subbundle $D$ is proportional to the Levi form. In particular, we give a classification of pseudo-Einstein Hopf-hypersurfaces in a non-flat complex space form.
"Pseudo-Einstein CR-structures on real hypersurfaces in a complex space form." Hokkaido Math. J. 37 (1) 1 - 17, February 2008. https://doi.org/10.14492/hokmj/1253539581