PARALLEL SUBMANIFOLDS OF THE REAL 2-GRASSMANNIAN

Jentsch, Tillmann

doi:info:doi/10.18910/29203

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タイトル	PARALLEL SUBMANIFOLDS OF THE REAL 2-GRASSMANNIAN
著者	Jentsch, Tillmann Jentsch, Tillmann
抄録	A submanifold of a Riemannian symmetric space is called parallel if its second fundamental form is parallel. We classify parallel submanifolds of the Grassmannian G_2^+ (R^<n + 2>) which parameterizes the oriented 2-planes of the Euclidean space R^<n + 2>. Our main result states that every complete parallel submanifold of G_2^+ (R^<n + 2>), which is not a curve, is contained in some totally geodesic submanifold as a symmetric submanifold. The analogous result holds if the ambient space is the Riemannian product of two Euclidean spheres of equal curvature or the non-compact dual of one of the previously considered spaces. We also give a characterization of parallel submanifolds with curvature isotropic tangent spaces of maximal possible dimension in any symmetric space of compact or non-compact type.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	51
号	2
開始ページ	285
終了ページ	336
刊行年月	2014-04
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/29203
言語	英語
DOI	info:doi/10.18910/29203

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.51(2) P.285-P.336
DC.title	PARALLEL SUBMANIFOLDS OF THE REAL 2-GRASSMANNIAN
DC.creator	Jentsch, Tillmann
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2014-04
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/29203
DCTERMS.abstract	A submanifold of a Riemannian symmetric space is called parallel if its second fundamental form is parallel. We classify parallel submanifolds of the Grassmannian G_2^+ (R^<n + 2>) which parameterizes the oriented 2-planes of the Euclidean space R^<n + 2>. Our main result states that every complete parallel submanifold of G_2^+ (R^<n + 2>), which is not a curve, is contained in some totally geodesic submanifold as a symmetric submanifold. The analogous result holds if the ambient space is the Riemannian product of two Euclidean spheres of equal curvature or the non-compact dual of one of the previously considered spaces. We also give a characterization of parallel submanifolds with curvature isotropic tangent spaces of maximal possible dimension in any symmetric space of compact or non-compact type.
DC.identifier	info:doi/10.18910/29203
citation_title	PARALLEL SUBMANIFOLDS OF THE REAL 2-GRASSMANNIAN
citation_author	Jentsch, Tillmann
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2014-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	51
citation_issue	2
citation_firstpage	285
citation_lastpage	336
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/29203
citation_doi	info:doi/10.18910/29203

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