ON THE CLASSIFICATION OF HOMOGENEOUS 2-SPHERES IN COMPLEX GRASSMANNIANS

Fei, Jie; Jiao, Xiaoxiang; Xiao, Liang; Xu, Xiaowei

doi:info:doi/10.18910/24475

このアイテムのアクセス数:33件（2020-09-25 06:45 集計）

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タイトル	ON THE CLASSIFICATION OF HOMOGENEOUS 2-SPHERES IN COMPLEX GRASSMANNIANS
著者	Fei, Jie Fei, Jie
	Jiao, Xiaoxiang Jiao, Xiaoxiang
	Xiao, Liang Xiao, Liang
	Xu, Xiaowei Xu, Xiaowei
抄録	In this paper we discuss a classification problem of homogeneous 2-spheres in the complex Grassmann manifold G(kC1, nC1) by theory of unitary representations of the 3-dimensional special unitary group SU(2). First we observe that if an immersion x W S＾2 ! G(k C 1, n C 1) is homogeneous, then its image x(S＾2) is a 2-dimensional _(SU(2))-orbit in G(k C1, nC1), where _W SU(2)!U(nC1) is a unitary representation of SU(2). Then we give a classification theorem of homogeneous 2-spheres in G(k C1, n C1). As an application we describe explicitly all homogeneous 2-spheres in G(2, 4). Also we mention about an example of non-homogeneous holomorphic 2-sphere with constant curvature in G(2, 4).
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	50
号	1
開始ページ	135
終了ページ	152
刊行年月	2013-03
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/24475
言語	英語
DOI	info:doi/10.18910/24475
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 1　(2013-3）

著者版フラグ	publisher
NII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.50(1) P.135-P.152
DC.title	ON THE CLASSIFICATION OF HOMOGENEOUS 2-SPHERES IN COMPLEX GRASSMANNIANS
DC.creator	Fei, Jie
	Jiao, Xiaoxiang
	Xiao, Liang
	Xu, Xiaowei
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2013-03
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/24475
DCTERMS.abstract	In this paper we discuss a classification problem of homogeneous 2-spheres in the complex Grassmann manifold G(kC1, nC1) by theory of unitary representations of the 3-dimensional special unitary group SU(2). First we observe that if an immersion x W S＾2 ! G(k C 1, n C 1) is homogeneous, then its image x(S＾2) is a 2-dimensional _(SU(2))-orbit in G(k C1, nC1), where _W SU(2)!U(nC1) is a unitary representation of SU(2). Then we give a classification theorem of homogeneous 2-spheres in G(k C1, n C1). As an application we describe explicitly all homogeneous 2-spheres in G(2, 4). Also we mention about an example of non-homogeneous holomorphic 2-sphere with constant curvature in G(2, 4).
DC.identifier	info:doi/10.18910/24475
citation_title	ON THE CLASSIFICATION OF HOMOGENEOUS 2-SPHERES IN COMPLEX GRASSMANNIANS
citation_author	Fei, Jie
	Jiao, Xiaoxiang
	Xiao, Liang
	Xu, Xiaowei
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-03
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	1
citation_firstpage	135
citation_lastpage	152
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/24475
citation_doi	info:doi/10.18910/24475

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