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On the second Betti number of a compact Sasakian space
http://hdl.handle.net/10083/2132
http://hdl.handle.net/10083/2132d798e513-844c-427a-827c-093ec6b2ce08
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
KJ00004829633.pdf (270.1 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2008-04-30 | |||||
| タイトル | ||||||
| タイトル | On the second Betti number of a compact Sasakian space | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Tachibana, Shun-ichi
× Tachibana, Shun-ichi× Ogawa, Yosuke× 立花, 俊一× 小川, 洋輔 |
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| 著者(ヨミ) | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 69713 | |||||
| 姓名 | タチバナ, シュンイチ | |||||
| 著者(ヨミ) | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 69714 | |||||
| 姓名 | オガワ, ヨウスケ | |||||
| 内容記述 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | 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\ ions 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]. |
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| 書誌情報 |
お茶の水女子大學自然科學報告 巻 17, 号 2, p. 27-32, 発行日 1966-12 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 00298190 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AN00033958 | |||||
| フォーマット | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | application/pdf | |||||
| 形態 | ||||||
| 270051 bytes | ||||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 400 | |||||
| 出版者 | ||||||
| 出版者 | お茶の水女子大学 | |||||
| 資源タイプ | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | 紀要論文 | |||||
| 資源タイプ・ローカル | ||||||
| 紀要論文 | ||||||
| 資源タイプ・NII | ||||||
| Departmental Bulletin Paper | ||||||
| 資源タイプ・DCMI | ||||||
| text | ||||||
| 資源タイプ・ローカル表示コード | ||||||
| 03 | ||||||
| 所属 | ||||||
| Department of Mathematics, Faculty of Science, Ochanomizu University | ||||||
| 所属 | ||||||
| Department of Mathematics, Faculty of Science, Ochanomizu University | ||||||
