| Project/Area Number |
14540085
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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 | Saga University |
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Principal Investigator |
CHENG Qing-ming Saga Univ., Fac.of Sci.and Eng., Prof, 理工学部, 教授 (50274577)
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| Co-Investigator(Kenkyū-buntansha) |
SHIOHAMA Katsuhiro Saga Univ., Fac.of Sci.and Eng., Prof, 理工学部, 教授 (20016059)
ISHIKAWA Susumu Saga Univ., Fac.of Sci.and Eng., Prof, 理工学部, 教授 (10039258)
KAWAI Shigeo Saga Univ., Fac.of Sci.and Eng., Prof, 文化教育学部, 教授 (30186043)
MATSUZOE Hiroshi Saga Univ., Fac.of Sci.and Eng., Ass.Prof, 理工学部, 助教授 (90315177)
MASHIKO Yukihiro Saga Univ., Fac.of Sci.and Eng., Lecture, 理工学部, 講師 (00315178)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | complete submanifod / mean curvature / scalar curvature / eigen values of Laplacian / Ricci curvature / sectional curvature / Euclidean space and sphere / homogeneous manifold / Laplacian / eigenvalue / complete minimail hypersuface / harmonic stability / statistical manifold / sphere / constant mean curvature / complete hypersuface / fundamental group / first eigen value of p-Laplacian / Euclidean space / complete submanifolds / Gauss-Kronecker curvature / radial curvature / maximal diameter theorem / differentiable sphere theorem |
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| Research Abstract |
In this project, we mainly investigated the curvature structures and topological structures of submanifolds in Riemannian manifolds and the geometry of eigenvalues and eigenfunctions of Laplacian on Riemannian manifolds. It is our purpose to research geometric problems on properties oftopology and curvatures of many kinds of manifolds by means of many different methods. We studied (1)the geometry of topological structures and curvature structures of submanifolds in Euclidean spaces and spheres. (2)the geometry of compact hypersurfaces with infinite fundamental group in spheres. (3)the geometry of curvature structures of complete hypersurfaces in 4-dimensional space forms. (4)the geometry of curvature structures of complete space-like hypersurfaces in Lorentz spaces. (5)the geometry ofeigenvalues and eigenfunctions of Laplacian on Riemannian manifolds. (6)the geometry of sphere theorems. (7)the geometry of conformally projective structures of satistical manifolds. (8)the geometry on radial curvature and topology of manifolds and obtained many important results.
It is characterizations of our project that important contributions on the research of topological structures and curvature structures of complete submanifolds in Riemannian manifolds are obtained. Furthermore, Cheng and Yang obtained important results for the investigation on eigenvalues of Laplacian on Riemannian manifolds.
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