GEOMETRY OF LAPLACE OPERATOR OR ITS VARIATION TYPE OPERATOR ON RIEMANNIAN MANIFOLD (2003)
| Project/Area Number |
12640078
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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 |
ISHIKAWA Susumu SAGA UNIV., MATHEMATICS, PROFESSOR, 理工学部, 教授 (10039258)
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| Co-Investigator(Kenkyū-buntansha) |
SHIOHAMA Katsuhiro SAGA UNIV., MATHEMATICS, PROFESSOR, 理工学部, 教授 (20016059)
KUROGI Tetsunori FUKUI UNIV., MATHEMATICS, PROFESSOR, 教育地域, 教授 (90022681)
KAWAI Shigeo SAGA UNIV., MATHEMATICS, PROFESSOR, 文化教育学部, 教授 (30186043)
CHENG Qing-ming SAGA UNIV., MATHEMATICS, PROFESSOR, 理工学部, 教授 (50274577)
YAMADA Kotaro KYUSHU UNIV., MATHEMATICS, PROFESSOR, 数理学, 教授 (10221657)
猿子 幸弘 佐賀大学, 理工学部, 講師 (00315178)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2003: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2000: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | Finite type submanifold / Biharmonic submanifold / Minimal submanifold / 部分多様体論 / 極小曲面論 / 共形幾何学 / 有限型多様体 / 二重調和多様体 |
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| Research Abstract |
We tried to investigate the following themes or questions with concernig of the finite type submanifolds or biharmonic submanifolds :
(i)Are there the finite type surfaces with given mean curvature H in the family of surfaces of revolution x.(u, v)=(u cos v, u sin v, f(u)) generated by the periodic function z=f(u) ?
(ii)Are there the finite type surfaces with given Gauss curvature K in the family of surfaces of revolution x(u, v)=(u cos v, u sin v, f(u)) generated by the function z=f(u) ?
(iii)Are there the finite type surfaces with constant mean curvature in the family of surfaces ?
(iv)Are there the Willmore surfaces of finite type ?
(v-1)The finite type submanifolds in the space with D` Atri metric.
(v-2)The biharmonic submanifolds in the space with D` Atri metric
We will continue to study in future the following still open conjectures of Prof. Bang-yen Chen
1.To determine all of the finite type surfaces in Eucldean space of dimension 3
(Chen conjectur 1 : The only finite type surfaces in Eucldean space of dimension 3 are the minimal suefaces, spheres and right cylinders.)
2.To determine all of the biharmonic submanifolds in Eucldean space of dimension n
(Chen conjectur 2 : The only in Eucldean space of dimension n (n>3) are the harmonc ones.)
3.To determine all of the biharmonic submanifolds in Minkowsky space of dimension 4.
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Report
(5 results)
Research Products
(35 results)
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[Journal Article] Hypersurfaces in Euclidean spaces2001
Author(s)
Qing-Ming Cheng
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Journal Title
Hypersurfaces in Euclidean spaces Proc.Fifth Pacific Rim Geom.Conference, Tohoku University, Sensai, Japan.(Tohoku Math.Publ.) 20
Pages: 33-42
Description
「研究成果報告書概要(欧文)」より
Related Report
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[Journal Article] Sphere Theorems2000
Author(s)
Katsuhiro Shiohama
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Journal Title
Handbook of Differential Geometry, Chapter 8, (Edited by G.Dillen, P.Verstraelen) Vol.1
Pages: 867-903
Description
「研究成果報告書概要(欧文)」より
Related Report
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