Classification of f-biharmonic submanifolds in Lorentz space forms

In this paper, -biharmonic submanifolds with parallel normalized mean curvature vector field in Lorentz space forms are discussed. When is a constant, we prove that such submanifolds have parallel mean curvature vector field with the minimal polynomial of the shape operator of degree . When is a fun...

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 19; no. 1; pp. 1299 - 1314
Main Author Du, Li
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 31.12.2021
De Gruyter Poland
Subjects
53C40
biharmonic submanifolds
Curvature
f-biharmonic submanifolds
Fields (mathematics)
Lorentz space forms
Manifolds (mathematics)
Mathematical analysis
parallel normal mean curvature vector field
Polynomials
pseudo-umbilical
the shape operator
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Summary:In this paper, -biharmonic submanifolds with parallel normalized mean curvature vector field in Lorentz space forms are discussed. When is a constant, we prove that such submanifolds have parallel mean curvature vector field with the minimal polynomial of the shape operator of degree . When is a function, we completely classify such pseudo-umbilical submanifolds.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2021-0084