| Project/Area Number |
12304005
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | Kobe University |
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Principal Investigator |
SASAKI Takeshi Kobe University, Faculty of Science, Professor, 理学部, 教授 (00022682)
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| Co-Investigator(Kenkyū-buntansha) |
OHNITA Yoshihiro Tokyo Metropolitan University, Grad.School of Science, Professor, 大学院・理学研究科, 教授 (90183764)
SAKANE Yuusuke Osaka University, Grad.School of Inform.Sci.Techn., Professor, 大学院・情報科学研究科, 教授 (00089872)
YOSHIDA Masaaki Kyushu University, Grad.School of Math.Science, Professor, 大学院・数理学研究科, 教授 (30030787)
YAMAGUCHI Keizo Hokkaido University, Grad.School of Science, Professor, 大学院・理学研究科, 教授 (00113639)
MIYAOKA Reiko Kyushu University, Grad.School of Math.Science, Professor, 大学院・数理学研究科, 教授 (70108182)
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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 |
¥28,710,000 (Direct Cost: ¥23,400,000、Indirect Cost: ¥5,310,000)
Fiscal Year 2003: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Fiscal Year 2002: ¥7,020,000 (Direct Cost: ¥5,400,000、Indirect Cost: ¥1,620,000)
Fiscal Year 2001: ¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2000: ¥5,700,000 (Direct Cost: ¥5,700,000)
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| Keywords | geometric structure / minimal surface / hypergeometric differential equation / integrable system / harmonic map constant / mean curvature surface / projective submanifold / line congruence |
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| Research Abstract |
The result of the project is summarized as follows :
1. Construction of a canonical projective immersion of the moduli space of marked cubic surfaces and determination of the uniformization equation
2. Study of shape of the image of Schwarz map defined by the Gauss differential equation with purely imaginary exponents
3. Study of transformations of projective surfaces such as projectively minimal surfaces and relation with line congruence and differential invariants; special surfaces defined by Appell's differential sytems
4. Computation of the harmonic cohomology of compact symplectic nilmanifolds and construction of distinct symplectic structures on such manifolds
5. Classification of CMC surfaces in H^3 and R^3 by the DPW method and explicit construction of discrete CMC surfaces
6. Determination of the condition that the mean curvature of rotation surface is periodic in terms of the integral of the mean curvature
7. Proposal of pluri-harmonic mapping of finite type making use of algebraic integrable systems
8. Formulation of variational problem of thin films under the gravity and study of stability of solutions
9. Unified method of solving sinh-Gordon, Liouville, and cosh-Gordon equation and construction of Backlund transformation of solutions
10. Implementation of prime decomposition of polynomial ideals over small finite fields
11. Introduction and study of the kappa function defined by j(k(r))=(r)
12. Definition of the notion of flat fronts for flat surfaces with singular points in 3-dimensional hyperbolic space and development of its theory
13. Proof of rigidity of projective immersions of Hermitian symmetric spaces not necessarily irreducible
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