{"title":"The energy density of biharmonic quadratic maps between spheres","authors":"Rareş Ambrosie, Cezar Oniciuc","doi":"10.1016/j.difgeo.2023.102096","DOIUrl":null,"url":null,"abstract":"<div><p><span>In this paper, we first prove that a quadratic form from </span><span><math><msup><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mi>m</mi></mrow></msup></math></span> to <span><math><msup><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mi>n</mi></mrow></msup></math></span> is non-harmonic biharmonic if and only if it has constant energy density <span><math><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></span>. Then, we give a positive answer to an open problem raised in <span>[1]</span> concerning the structure of non-harmonic biharmonic quadratic forms. As a direct application, using classification results for harmonic quadratic forms, we infer classification results for non-harmonic biharmonic quadratic forms.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001225","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we first prove that a quadratic form from to is non-harmonic biharmonic if and only if it has constant energy density . Then, we give a positive answer to an open problem raised in [1] concerning the structure of non-harmonic biharmonic quadratic forms. As a direct application, using classification results for harmonic quadratic forms, we infer classification results for non-harmonic biharmonic quadratic forms.
期刊介绍:
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.