{"title":"On minimality and scalar curvature of CMC triharmonic hypersurfaces in pseudo-Riemannian space forms","authors":"Li Du, Yong Luo","doi":"10.1007/s10231-023-01422-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we first study the minimality of triharmonic hypersurfaces with constant mean curvature in pseudo-Riemannian space forms under the assumption that the shape operator is diagonalizable. Then, we prove that such nonminimal hypersurfaces have constant scalar curvature. As its applications, we estimate the constant scalar curvature and the constant mean curvature.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-023-01422-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we first study the minimality of triharmonic hypersurfaces with constant mean curvature in pseudo-Riemannian space forms under the assumption that the shape operator is diagonalizable. Then, we prove that such nonminimal hypersurfaces have constant scalar curvature. As its applications, we estimate the constant scalar curvature and the constant mean curvature.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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