| Project/Area Number |
16204007
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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 | Tohoku University (2006)
Kyushu University (2004-2005) |
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Principal Investigator |
MIYAOKA Reiko Tohoku University, Graduate School of Scineces, Prof. (70108182)
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Kotaro Kyushu Univ., Graduate School of Mathematics, Prof. (10221657)
IWASAKII Katunori Kyushu Univ., Graduate School of Mathematics, Prof. (00176538)
KAJIWARA Kenji Kyushu Univ., Graduate School of Mathematics, Prof. (40268115)
NAKAYASHIKI Atsushi Kyushu Univ., Graduate School of Mathematics, Assoc. Prof. (10237456)
NAGATOMO Yasuyuki Kyushu Univ., Graduate School of Mathematics, Assoc. Prof. (10266075)
大津 幸男 九州大学, 大学院・数理学研究院, 助教授 (80233170)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥34,970,000 (Direct Cost: ¥26,900,000、Indirect Cost: ¥8,070,000)
Fiscal Year 2006: ¥11,050,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥2,550,000)
Fiscal Year 2005: ¥9,620,000 (Direct Cost: ¥7,400,000、Indirect Cost: ¥2,220,000)
Fiscal Year 2004: ¥14,300,000 (Direct Cost: ¥11,000,000、Indirect Cost: ¥3,300,000)
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| Keywords | isoparametric hypersurfaces / G2 orbits / Painleve equation / Moduli of singularities / Theory of harmonic maps / Yang-Mills connection / Einstein metric / quantum cohomology / G_2軌道 / 極小曲面のガウス写像 / 特異点の解析 / Painleve方程式 / 超楕円ヤコビ多様体 / 四元数ケーラー多様体 / Frobenius多様体 / Lagrange部分多様体 / 摂動スカラー曲率 / モデュライ理論 / 主編極アーベル多様性 / ツイスター切断理論 / 4元数対称空間 / 特異ルジャンドル曲線 |
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| Research Abstract |
Miyaoka gives a new proof for the Dorfmeister Neher classification theorem on isoparametric hypersurfaces, and as applications of hypersurface geometry, clarifies the topological structure of the anti-self-dual bundle of complex projective plane and complete austere submanifolds, constructs Ricci flat metrics, special Lagrangian submanifolds. She also gets twister fibrations from the geometry of G2 orbits. Iwasaki connects the algebraic formulation of Painleve IV with the ergodic theory of birational maps of algebraic surfaces via Riemann-Hilbert correspondence, and shows the chaotic behavior of non-linear monodoromy. Kajiwara applies the theoretic formulation of the Painleve systems and constructs the determinant formula of the hypergeometric solutions of q-Painleve, and relates it with the solutions of the associate linear problems. Nakayashiki characterizes the coefficients of the series of sigma function by those of defining functions of the algebraic curves. Nagatomo obtains an es
… More
sential relation between harmonic maps and the Yang-Mills connections, and generalizes Takahashi's theorem, de Carom-Wallach's theorem, and constructs harmonic maps from quaternion Kaehler manifold to Grassmannian manifolds. Yamada-Umehara-Rossman classify the behavior of the ends of complete flat fronts in the hyperbolic 3-space. Fujioka studies integrability and periodicity of the motion of curves in complex hyperbolics which depend on Burger's equation and have descritization. Ishikawa classifies singularities of inproper affine surfaces and surfaces with constant Gauss curvature, and their dual surfaces. He also clarifies moduli of the singularities, and obtains a relation between plane curves and their Legendle curves. Udagawa classifies compact isotropic submanifolds with parallel mean curvature vector wit the sectional curvature. Tamaru proves a fixed point theorem for cohomogeneity one action corresponding to homogeneous hypersurfaces in symmetric spaces of non-compact type. Matsuura studies a development of plane curves depending on KdV equation w..r.t. discrete time. Ikeda studies equi-energy surfaces of characteristic manifod of Whittaker abel group and full Kostant-Toda lattice via micro-local anaysis. Guest investigates harmonic maps, quantum cohomorogy and mirror symmetry, and writes an introductory book Futaki proves the existence of Sasaki-Einstein metrics on some toric Sasakian manifolds, in particular, the existence of compelete Ricci-flat metric on the canonical bundles of toric Fano manifolds. Less
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