CLASSIFICATION OF HOMOGENEOUS WILLMORE SURFACES IN S^n

Dorfmeister, Josef; Wang, Peng

doi:https://doi.org/10.18910/77231

アクセス数:104件（2024-05-18 19:14 集計）

固定URL: https://doi.org/10.18910/77231

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タイトル	CLASSIFICATION OF HOMOGENEOUS WILLMORE SURFACES IN S^n
著者	著者名 Dorfmeister, Josef
著者	著者名 Wang, Peng
抄録	In this note we consider homogeneous Willmore surfaces in S^＜n+2＞. The main result is that a homogeneous Willmore two-sphere is conformally equivalent to a homogeneous minimal twosphere in S^＜n+2＞, i.e., either a round two-sphere or one of the Borůvka-Veronese 2-spheres in S^＜2m＞. This entails a classification of all Willmore CP^1 in S^＜2m＞. As a second main result we show that there exists no homogeneous Willmore upper-half plane in S^＜n+2＞ and we give, in terms of special constant potentials, a simple loop group characterization of all homogeneous surfaces which have an abelian transitive group.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	57(4)
ページ	805-817
刊行年月	2020-10
言語	英語
ハンドルURL	https://hdl.handle.net/11094/77231
DOI	https://doi.org/10.18910/77231
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 57, Number 4 （2020-10）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2020, 57(4), p. 805-817
DC.title	CLASSIFICATION OF HOMOGENEOUS WILLMORE SURFACES IN S^n
DC.creator	Dorfmeister, Josef
DC.creator	Wang, Peng
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2020-10
DCTERMS.abstract	In this note we consider homogeneous Willmore surfaces in S^＜n+2＞. The main result is that a homogeneous Willmore two-sphere is conformally equivalent to a homogeneous minimal twosphere in S^＜n+2＞, i.e., either a round two-sphere or one of the Borůvka-Veronese 2-spheres in S^＜2m＞. This entails a classification of all Willmore CP^1 in S^＜2m＞. As a second main result we show that there exists no homogeneous Willmore upper-half plane in S^＜n+2＞ and we give, in terms of special constant potentials, a simple loop group characterization of all homogeneous surfaces which have an abelian transitive group.
DC.identifier	10.18910/77231
DC.format	77231
citation_title	CLASSIFICATION OF HOMOGENEOUS WILLMORE SURFACES IN S^n
citation_author	Dorfmeister, Josef
citation_author	Wang, Peng
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2020-10
citation_journal_title	Osaka Journal of Mathematics
citation_volume	57
citation_issue	4
citation_firstpage	805
citation_lastpage	817
citation_public_url	https://hdl.handle.net/11094/77231
citation_doi_detail	10.18910/77231
citation_doi	https://doi.org/10.18910/77231

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