非平面复数空间形式中霍普夫超曲面的新特征

Pub Date : 2024-07-05 DOI:10.1007/s10998-024-00604-2

Wenjie Wang

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引用次数: 0

摘要

研究证明，如果且只有当超曲面是霍普夫（Hopf）超曲面时，非平面复空间形式的实超曲面的（*\）-里奇算子才是里布平行算子。作为这一结果的应用，我们得到了具有平行（*\）-Ricci 算子的实超曲面的分类定理。这些结果回答了凯马卡米斯（Kaimakamis）和帕纳吉奥蒂杜（Panagiotidou）十年前提出的一些悬而未决的问题。

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New characterization of Hopf hypersurfaces in nonflat complex space forms

It is proved that the \(*\)-Ricci operator of a real hypersurface in a nonflat complex space form is Reeb parallel if and only if the hypersurface is Hopf. As an application of this result, we obtain a classification theorem of real hypersurfaces with parallel \(*\)-Ricci operators. These results answer some open questions posed by Kaimakamis and Panagiotidou a decade ago.

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