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Nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in $\mathbb {C}P^{2}$ and $\mathbb {C}H^{2}$

Part of: Local differential geometry Global differential geometry

Published online by Cambridge University Press:  14 August 2023

Qianshun Cui  and
Zejun Hu Open the ORCID record for Zejun Hu [Opens in a new window]
Qianshun Cui
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, P.R. China e-mail: cuiqianshun@gs.zzu.edu.cn
Zejun Hu*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, P.R. China e-mail: cuiqianshun@gs.zzu.edu.cn
*
e-mail: huzj@zzu.edu.cn
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Abstract

In this paper, we solved an open problem raised by Cecil and Ryan (2015, Geometry of Hypersurfaces, Springer Monographs in Mathematics, Springer, New York, p. 531) by proving the nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in $\mathbb {C}P^{2}$ and $\mathbb {C}H^{2}$.

Keywords

Nonflat complex planesRicci-semisymmetricnon-Hopf hypersurface

MSC classification

Primary: 53B25: Local submanifolds 53C30: Homogeneous manifolds
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 1 , March 2024 , pp. 188 - 200
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

This work was supported by the National Natural Science Foundation of China (Grant No. 12171437).

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