APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES

Kondo, Kei; Tanaka, Minoru

doi:https://doi.org/10.18910/25094

APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES

Kondo, Kei; Tanaka, Minoru

Osaka Journal of Mathematics, 2013, 50(2), 541-562

アクセス数:257件（2025-07-06 07:08 集計）

固定URL: https://doi.org/10.18910/25094

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タイトル	APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES
著者	NRID 1000070736123 1000070736123 著者名 Kondo, Kei
著者	NRID 1000010112773 1000010112773 著者名 Tanaka, Minoru
抄録	Recently we generalized Toponogov's comparison theorem to a complete Riemannian manifold with smooth convex boundary, where a geodesic triangle was replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface was replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary. The aim of this article is to prove splitting theorems of two types as an application. Moreover, we establish a weaker version of our Toponogov comparison theorem for open triangles, because the weaker version is quite enough to prove one of the splitting theorems.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	50(2)
ページ	541-562
刊行年月	2013-06
言語	英語
ハンドルURL	https://hdl.handle.net/11094/25094
DOI	https://doi.org/10.18910/25094
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 50, Number 2　(2013-6）

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. 2013, 50(2), p. 541-562
DC.title	APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES
DC.creator	Kondo, Kei
DC.creator	Tanaka, Minoru
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	2013-06
DCTERMS.abstract	Recently we generalized Toponogov's comparison theorem to a complete Riemannian manifold with smooth convex boundary, where a geodesic triangle was replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface was replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary. The aim of this article is to prove splitting theorems of two types as an application. Moreover, we establish a weaker version of our Toponogov comparison theorem for open triangles, because the weaker version is quite enough to prove one of the splitting theorems.
DC.identifier	10.18910/25094
DC.format	25094
citation_title	APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES
citation_author	Kondo, Kei
citation_author	Tanaka, Minoru
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-06
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	2
citation_firstpage	541
citation_lastpage	562
citation_public_url	https://hdl.handle.net/11094/25094
citation_doi_detail	10.18910/25094
citation_doi	https://doi.org/10.18910/25094

APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES

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