| Project/Area Number |
12440021
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Saga University |
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Principal Investigator |
SHIOHAMA K. Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (20016059)
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| Co-Investigator(Kenkyū-buntansha) |
SHIOYA T. Tohoku Univ. Grand. School. Science, Assoc. Prof., 大学院・理学研究科, 助教授 (90235507)
ENOMOTO K. Tokyo Science Univ., Fac. Basic Engineering, Assoc. Prof., 基礎工学部, 助教授 (40194005)
SUYAMA Y. Fukuoka Univ., Fac. Science, Math. Dept. Professor, 理学部, 教授 (70028223)
OTSU Y. Kyushu Univ., Grad. School of Math., Assoc. Prof., 大学院・数理学研究科, 助教授 (80233170)
町頭 義朗 大阪教育大学, 教育学部, 助教授 (00253584)
後藤 ミドリ 福岡工業大学, 情報工学部, 教授 (60162161)
猿子 幸弘 佐賀大学, 理工学部, 助手 (00315178)
石川 晋 佐賀大学, 理工学部, 教授 (10039258)
成 慶明 城西大学, 理学部, 助教授 (50274577)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥9,100,000 (Direct Cost: ¥9,100,000)
Fiscal Year 2002: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2001: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2000: ¥3,400,000 (Direct Cost: ¥3,400,000)
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| Keywords | Riemannian manifolds / Curvature / Geodesics / Submanifolds / Alexandrov spaces / 2nd. Fundamental form / Hansdorff convergence / 凸関数 / 球面 / 共形幾何学 / 放射曲率 |
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| Research Abstract |
Many of our results are concerned with Riemannian geometry and the geometry of submanifolds. Spaces of constant curvature, such as spheres and Euclidean spaces, are the main models and reference spaces. We have greatly changed the models to wider classes of metrics. The Alexandrov-Toponogov comparison theorems for geodesic triangles on complete manifolds with base point at 0, whose radial curvature is bounded below by that of a model surface with rotationally symmetric metric have been established. Complete hypersurfaces with constant scalar curvature have also been investigated in details. The scaling limits of pointed complete open manifolds with asymptotically nonnegative radial curvature has been investigated.
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