Radial curvature and topology of Riemannian manifolds
| Project/Area Number |
19540107
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Fukuoka University |
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Principal Investigator |
SHIOHAMA Katsuhiro Fukuoka University, 理学部, 非常勤講師研究者 (20016059)
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| Co-Investigator(Kenkyū-buntansha) |
SUYA Yoshihiko 福岡大学, 理学部, 教授 (70028223)
ISHIKAWA Susumu 福岡工業大学, 情報工学部, 教授 (10039258)
KAWAKUBO Satoshi 福岡大学, 理学部, 助教 (80360303)
MATSUURA Nozomu 福岡大学, 理学部, 助教 (00389339)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | リーマン計量 / 曲率 / 測地線 / 放射曲率 / リッチ曲率 / ハウスドルフ距離 |
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| Research Abstract |
The angle comparison theorem plays an important role for the study of the radial curvature and topology of pointed complete Riemannian manifolds. We have proved that the angle comparison for all the angles of all the generic geodesic triangles is valid. We are led to a new idea by thinking of radially curved manifolds as certain complete real hypersurfaces on the compat rank one symmetric spaces. This corresponds to the maximal diameter theorem for compact manifolds with positive curvature. Thus the global characterization of certain complete real hyprsurfaces are obtained.
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Report
(5 results)
Research Products
(23 results)
