# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 37 (2008) pp.1-17

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### Abstract

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.

MSC(Primary) 53C15(MSC2000), 53B20(MSC2000), 53C25(MSC2000) real hypersurfaces, complex space forms, the g.-Tanaka-Webster connection, pseudo-Einstein structures, g.-Tanaka-Webster flat structures.