Development and relations between various geometries and integrable systems

Miyaoka给出了等参超曲面上的Dorfmeister Neher分类定理的一个新证明，并作为超曲面几何的应用，阐明了复射影平面和完备素子流形的反自对偶丛的拓扑结构，构造了Ricci平坦度量和特殊的拉格朗日子流形。她还从G2轨道的几何形状中获得了扭曲的纤毛。岩崎通过Riemann-Hilbert对应将Painleve IV的代数形式与代数曲面的二次映射的遍历理论联系起来，并展示了非线性单调的混沌行为。Kajiwara应用Painleve系统的理论公式，构造了Q-Painleve超几何解的行列式，并将其与相关线性问题的解联系起来。Nakayashiki用定义代数曲线的函数的系数来刻画sigma函数级数的系数。长岛获得Es…推广了Takahashi定理、de Carom-Wallach定理，构造了从四元数Kaehler流形到Grassman流形的调和映射。Yamada-Umehara-Rossman对双曲三维空间中完全平坦前锋的端部行为进行了分类。Fujioka研究了复双曲中曲线运动的可积性和周期性，它依赖于Burger方程并具有描述性。Ishikawa对非真仿射曲面和常高斯曲率曲面及其对偶曲面的奇点进行了分类。他还阐明了奇点的模数，并得到了平面曲线与其Legendle曲线之间的关系。Udagawa对具有平行平均曲率向量和截面曲率的紧致迷向子流形进行分类。Tamaru证明了非紧型对称空间中与齐次超曲面对应的上齐次不动点定理。Matsuura研究了依赖于KdV方程的平面曲线的发展。离散时间。Ikeda通过微观局域分析研究了Whittaker-Abel群和全Kostant-Toda格的特征流形的等能曲面。Guest研究了调和映射、量子上同调和镜像对称性，并写了一本介绍性的书Futaki证明了一些环面Sasakian流形上的Sasaki-Einstein度量的存在性，特别是环面Fano流形的正则丛上的Compelee Ricci-Flat度量的存在性。较少

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