CLASSIFICATION OF ISOPARAMETRIC SUBMANIFOLDS ADMITTING A REFLECTIVE FOCAL SUBMANIFOLD IN SYMMETRIC SPACES OF NON-COMPACT TYPE

Koike, Naoyuki

doi:https://doi.org/10.18910/73746

アクセス数:184件（2024-09-01 08:55 集計）

固定URL: https://doi.org/10.18910/73746

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タイトル	CLASSIFICATION OF ISOPARAMETRIC SUBMANIFOLDS ADMITTING A REFLECTIVE FOCAL SUBMANIFOLD IN SYMMETRIC SPACES OF NON-COMPACT TYPE
著者	NRID 1000000281410 1000000281410 著者名 Koike, Naoyuki
抄録	In this paper, we assume that all isoparametric submanifolds have flat section. The main purpose of this paper is to prove that, if a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space of non-compact type admits a reflective focal submanifold and if it is of real analytic, then it is a principal orbit of a Hermann type action on the symmetric space. A hyperpolar action on a symmetric space of non-compact type admits a reflective singular orbit if and only if it is a Hermann type action. Hence is not extra the assumption that the isoparametric submanifold admits a reflective focal submanifold. Also, we prove that, if a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space of non-compact type satisfies some additional conditions, then it is a principal orbit of the isotropy action of the symmetric space, where we need not impose that the submanifold is of real analytic. We use the building theory in the proof.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	57(1)
ページ	207-246
刊行年月	2020-01
言語	英語
ハンドルURL	https://hdl.handle.net/11094/73746
DOI	https://doi.org/10.18910/73746
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 1 （2020-1）

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(1), p. 207-246
DC.title	CLASSIFICATION OF ISOPARAMETRIC SUBMANIFOLDS ADMITTING A REFLECTIVE FOCAL SUBMANIFOLD IN SYMMETRIC SPACES OF NON-COMPACT TYPE
DC.creator	Koike, Naoyuki
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	2020-01
DCTERMS.abstract	In this paper, we assume that all isoparametric submanifolds have flat section. The main purpose of this paper is to prove that, if a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space of non-compact type admits a reflective focal submanifold and if it is of real analytic, then it is a principal orbit of a Hermann type action on the symmetric space. A hyperpolar action on a symmetric space of non-compact type admits a reflective singular orbit if and only if it is a Hermann type action. Hence is not extra the assumption that the isoparametric submanifold admits a reflective focal submanifold. Also, we prove that, if a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space of non-compact type satisfies some additional conditions, then it is a principal orbit of the isotropy action of the symmetric space, where we need not impose that the submanifold is of real analytic. We use the building theory in the proof.
DC.identifier	10.18910/73746
DC.format	73746
citation_title	CLASSIFICATION OF ISOPARAMETRIC SUBMANIFOLDS ADMITTING A REFLECTIVE FOCAL SUBMANIFOLD IN SYMMETRIC SPACES OF NON-COMPACT TYPE
citation_author	Koike, Naoyuki
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2020-01
citation_journal_title	Osaka Journal of Mathematics
citation_volume	57
citation_issue	1
citation_firstpage	207
citation_lastpage	246
citation_public_url	https://hdl.handle.net/11094/73746
citation_doi_detail	10.18910/73746
citation_doi	https://doi.org/10.18910/73746

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