Quasi-Einstein hypersurfaces of complex space forms

TL;DR

This paper investigates quasi-Einstein hypersurfaces in non-flat complex space forms, providing classifications and extending understanding beyond Einstein hypersurfaces, with implications for gradient Ricci solitons.

Contribution

It offers a classification of quasi-Einstein hypersurfaces in complex Euclidean spaces and extends previous results on gradient Ricci solitons.

Findings

Classified quasi-Einstein hypersurfaces in complex Euclidean spaces.

Extended results on gradient Ricci solitons as special quasi-Einstein metrics.

Showed non-existence of Einstein hypersurfaces in non-flat complex space forms.

Abstract

Based on a well-known fact that there are no Einstein hypersurfaces in a non-flat complex space form, in this article we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hyersurface of a non-flat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of \cite{CK}.