Development and relations between various geometries and integrable systems

各种几何形状和可积系统之间的发展和关系

基本信息

批准号：
16204007
负责人：
MIYAOKA Reiko
金额：
$ 22.38万
依托单位：
Tohoku University (2006)Kyushu University (2004-2005)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

项目摘要

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

Miyaoka提供了有关异托马术超曲面的Dorfmeister Neher分类定理的新证明，并且作为超表面几何形状的应用，阐明了复杂的投影平面的反自我二线束的拓扑结构，并构建了Austere Submanifolds，并构建了Ricci Submanifolds，构建了Ricci Flat flater submanian submaniy submanifs sibmanifs sibmanifs sibmanifs submanifs sibmanifs sibmanifs sibmanifs sibmanifs sibmanifs。她还从G2轨道的几何形状中获得了Twister振动。 Iwasaki通过Riemann-Hilbert对应关系将Painleve IV的代数公式与代数表面的亿万富翁的千古理论联系起来，并显示了非线性单肌的混乱行为。 Kajiwara应用了Painleve系统的理论公式，并构建了Q-Painleve的超几何解的确定公式，并将其与关联线性问题的溶液相关联。 Nakayashiki通过定义代数曲线的函数的函数来表征一系列Sigma功能的系数。 Nagatomo在谐波图与Yang-Mills连接之间获得了更严重的关系，并概括了高桥定理，De Carom-Wallach的定理，并构建了Quaternion Kaehler歧管的谐波图到Grassmannian歧管。 Yamada-Omehara-Rossman对双曲线3空间中完整平面前部的末端的行为进行了分类。富士研究曲线在复杂的冬纤维化中的运动的整合和周期性，这取决于汉堡方程并具有描述。 Ishikawa对具有恒定高斯曲率及其双面表面的Inproper仿射表面和表面的奇异性进行了分类。他还阐明了模态的奇异性，并在平面曲线与其传奇曲线之间获得了关系。乌达瓦（Udagawa）将紧凑的各向同性亚策略与平均平均曲率向量进行分段曲率分类。塔玛鲁证明了同构性的固定点理论，该作用对应于非压缩类型的对称空间中的同质性超曲面。 Matsuura根据KDV方程W..R.T研究了平面曲线的发展。离散时间。 ikeda研究了通过微部位的Anaysis研究惠特克·亚伯组和全毛塔达晶格的特征性宣言。嘉宾调查了谐波图，量子同学和镜像对称性，并写了一本介绍书Futaki证明了Sasaki-Einstein指标的存在，尤其是Sasakian歧管，尤其是在Canonical fano fano歧管上的完整ricci-flat指标的存在。较少的