On non‐Hopf Ricci‐pseudosymmetric hypersurfaces in CP2$\mathbb {C}P^{2}$ and CH2$\mathbb {C}H^{2}$

Qianshun Cui and Zejun Hu

Mathematische Nachrichten, 2025, vol. 298, issue 2, 527-547

Abstract: In this paper, we study an open problem raised by Cecil and Ryan [Geometry of Hypersurfaces, Springer Monographs in Mathematics, p. 531] which asked whether there exist non‐Hopf Ricci‐pseudosymmetric hypersurfaces in CP2$\mathbb {C}P^{2}$ and CH2$\mathbb {C}H^{2}$. As our main results, we first prove the nonexistence of non‐Hopf Ricci‐pseudosymmetric hypersurfaces of the constant type in CH2$\mathbb {C}H^{2}$. Then, we prove the existence of non‐Hopf Ricci‐pseudosymmetric hypersurfaces of the constant type in CP2$\mathbb {C}P^{2}$. Finally, applying the preceding results and sharpening Theorem 4.1 of Wang and Zhang [J. Geom. Phys. 181 (2022), 104648], we prove the nonexistence of non‐Hopf weakly Einstein hypersurfaces with constant norm of Riemannian curvature tensor in both CP2$\mathbb {C}P^{2}$ and CH2$\mathbb {C}H^{2}$.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202300463

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:2:p:527-547

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().