{"title":"New characterization of Hopf hypersurfaces in nonflat complex space forms","authors":"Wenjie Wang","doi":"10.1007/s10998-024-00604-2","DOIUrl":null,"url":null,"abstract":"<p>It is proved that the <span>\\(*\\)</span>-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 <span>\\(*\\)</span>-Ricci operators. These results answer some open questions posed by Kaimakamis and Panagiotidou a decade ago.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-024-00604-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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