Quasi-Einstein Hypersurfaces of Complex Space Forms

Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi...

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Bibliographic Details
Published in:Advances in mathematical physics 2020, Vol.2020 (2020), p.1-9
Main Authors: Cui, Xuehui, Chen, Xiaomin
Format: Article
Language:English
Subjects:
Euclidean geometry
Euclidean space
Hyperspaces
Solitary waves
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Summary:Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat 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 Cho and Kimura.
ISSN:1687-9120
1687-9139
DOI:10.1155/2020/8891658