{"created":"2021-03-01T06:40:18.865743+00:00","id":34959,"links":{},"metadata":{"_buckets":{"deposit":"e2166d17-8d69-4a90-90db-3311f2081207"},"_deposit":{"id":"34959","owners":[],"pid":{"revision_id":0,"type":"depid","value":"34959"},"status":"published"},"_oai":{"id":"oai:teapot.lib.ocha.ac.jp:00034959","sets":["347:359:607"]},"item_11_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1966-12","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"32","bibliographicPageStart":"27","bibliographicVolumeNumber":"17","bibliographic_titles":[{"bibliographic_title":"お茶の水女子大學自然科學報告"}]}]},"item_11_description_17":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_11_description_46":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"紀要論文","subitem_description_type":"Other"}]},"item_11_description_7":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"Recently S.I. Goldberg [4] proved the following THEOREM A. If a compact, simply connected, regular 2m+1 dimensional Sasakian space has positive sectional curvature and its scalar curvature is constant, then it is isometric with a sphere S^<2m+1> with the natural structure. ?On the other hand the odd dimensional Betti number b_<2p+1>(M, R), 1≦2p+1≦m, of a compact Sasakian space M is even^1) and for the even dimensional Betti number of M the following theorem is known [4]. THEOREM B. If a compact, regular 2m +1 dimensional Sasakian space M has positive sectional curvature, then b_2(M, R)=0. ,The assumption \"regular\" in the theorems is essential, because the fibration of Boothby-Wang is used in their proofs. In this paper we shall prove the following theorem without the assumption \"regular\". THEOREM C. If any sectional curvature ρ(X, Y), of a complete 2m+1 (≧5). dimensional, Sasakian space M satisfies ρ(X, Y)>2m/1, then we have b_2(M, R)=0. REMARK. The metric of our Sasakian space is not normalized in the sence that the maximum sectional curvature is 1, though it has been normalized in a certain sence. As to the notat\\\nions we follow S. Tachibana [5] and give definitions, preliminary facts and formulas in §1 and §2. In §3-§5 we shall prove Theorem C by the method of Berger [2] and Bishop-Goldberg [3].","subitem_description_type":"Other"}]},"item_11_full_name_2":{"attribute_name":"著者(ヨミ)","attribute_value_mlt":[{"nameIdentifiers":[{"nameIdentifier":"69713","nameIdentifierScheme":"WEKO"}],"names":[{"name":"タチバナ, シュンイチ"}]},{"nameIdentifiers":[{"nameIdentifier":"69714","nameIdentifierScheme":"WEKO"}],"names":[{"name":"オガワ, ヨウスケ"}]}]},"item_11_publisher_36":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"お茶の水女子大学"}]},"item_11_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN00033958","subitem_source_identifier_type":"NCID"}]},"item_11_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"00298190","subitem_source_identifier_type":"ISSN"}]},"item_11_subject_20":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"400","subitem_subject_scheme":"NDC"}]},"item_11_text_18":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_text_value":"270051 bytes"}]},"item_11_text_47":{"attribute_name":"資源タイプ・ローカル","attribute_value_mlt":[{"subitem_text_value":"紀要論文"}]},"item_11_text_48":{"attribute_name":"資源タイプ・NII","attribute_value_mlt":[{"subitem_text_value":"Departmental Bulletin Paper"}]},"item_11_text_49":{"attribute_name":"資源タイプ・DCMI","attribute_value_mlt":[{"subitem_text_value":"text"}]},"item_11_text_50":{"attribute_name":"資源タイプ・ローカル表示コード","attribute_value_mlt":[{"subitem_text_value":"03"}]},"item_11_text_79":{"attribute_name":"所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematics, Faculty of Science, Ochanomizu University"},{"subitem_text_value":"Department of Mathematics, Faculty of Science, Ochanomizu University"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Tachibana, Shun-ichi"}],"nameIdentifiers":[{"nameIdentifier":"69711","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Ogawa, Yosuke"}],"nameIdentifiers":[{"nameIdentifier":"69712","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"立花, 俊一","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"69715","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"小川, 洋輔","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"69716","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-04-19"}],"displaytype":"detail","filename":"KJ00004829633.pdf","filesize":[{"value":"270.1 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KJ00004829633.pdf","url":"https://teapot.lib.ocha.ac.jp/record/34959/files/KJ00004829633.pdf"},"version_id":"9d319da1-b7f8-4a35-93a4-7112b2bdf01c"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"On the second Betti number of a compact Sasakian space","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"On the second Betti number of a compact Sasakian space"}]},"item_type_id":"11","owner":"1","path":["607"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-04-30"},"publish_date":"2008-04-30","publish_status":"0","recid":"34959","relation_version_is_last":true,"title":["On the second Betti number of a compact Sasakian space"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-12T05:39:46.232749+00:00"}