APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES

Kondo, Kei; Tanaka, Minoru

doi:info:doi/10.18910/25094

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タイトル	APPLICATIONS OF TOPONOGOV’S COMPARISON THEOREMS FOR OPEN TRIANGLES
著者	Kondo, Kei Kondo, Kei
著者	Tanaka, Minoru 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.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	50
号	2
開始ページ	541
終了ページ	562
刊行年月	2013-06
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/25094
言語	英語
DOI	info:doi/10.18910/25094

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(2) P.541-P.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
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2013-06
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/25094
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	info:doi/10.18910/25094
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_issn	00306126
citation_public_url	http://hdl.handle.net/11094/25094
citation_doi	info:doi/10.18910/25094

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