Global Study of Conformal Riemannian Structures

Shin Nayatani考虑了秩为1的对称空间的离散变换群在无穷远处边界上的作用，并研究了定义在不连续域上的正则不变度量。特别是，他将其应用于研究拓扑的商流形时，对称空间是复杂的双曲空间，并制定了四元数模拟CR结构/几何，将其应用于研究规范度量的quatenionic情况下。他还研究了几何结构的Furstenberg边界的一些高秩对称空间。芥川一夫研究调和映射从双曲空间到一定的不完整，负弯曲黎曼流形。特别是，他获得的结果的存在性，唯一性和规律性的解决方案的边值问题。他还对黎曼流形之间的极小映射进行了基础性研究，并得到了极小d的存在性和表示的结果。 ...更多信息 Izeki证明了共形平坦流形上平坦Hilbert空间丛的上同调的消失定理，并将其应用于极限集的Hausdorff维数的研究。Yasuhiro Nakagawa研究了Bando-Calabi-Futaki特征，这是Futaki特征的推广。他延长Futaki，森田的结果，解释Futaki字符作为Godbillon-Vey不变量，以案件的Bando-Calabi-Futaki字符。Seiki西川研究边值问题的调和映射之间的齐次黎曼流形的负曲率。特别是，他得到的结果的必要条件，边界值应满足，唯一性的解决方案和存在的解决方案的一个适当的边界值，在卡诺空间的情况下。坂藤茂利研究了存在问题爱因斯坦度量的Kahler流形和全纯向量丛以及它的关系的稳定性和退化现象。他还研究了奇异的几何结构出现的限制退化。少

Shin Nayatani considered the action of a discrete transformation group of a rank one symmetric space on its boundary at infinity, and studied a canonical invariant metric defined on the domain of discontinuity. In particular, he applied it to the study of the topology of the quotient manifold when the symmetric space is complex hyperbolic space, and also formulated the quaternionic analogue of CR structure/geometry, applying it to the study of the canonical metric in the quatenionic case. He also investigated geometric structures on the Furstenberg boundaries of some higher rank symmetric spaces.Kazuo Akutagawa studied harmonic maps from hyperbolic space to a certain incomplete, negatively curved Riemannian manifold. In particular, he obtained results on the existence, uniqueness and regularity of solutions for the boundary value problem. He also made fundamental research on minimal maps between Riemannian manifolds, and obtained results on the existence and representation of minimal d … More iffeomorphisms between hyperbolic disks.Hiroyasu Izeki proved a vanishing theorem for the cohomology of flat Hilbert space bundles over a conformally flat manifold, obtained as the quotient of a spherical domain by a Kleinian group, and applied it to the study of the Hausdorff dimension of the limit set.Yasuhiro Nakagawa investigated the Bando-Calabi-Futaki character, a generalization of the Futaki character. He extended Futaki-Morita's result that interpreted the Futaki character as a Godbillon-Vey invariant, to the case of the Bando-Calabi-Futaki character.Seiki Nishikawa studied the boundary value problem for hamonic maps between homogenious Riemannian manifolds of negative curvature. In particular, he obtained results on the necessary condition which the boundary value should satisfy, the uniqueness of solution and the existence of solution for a suitable boundary value, in the case of the Carnot spaces.Shigetoshi Bando studied the existence problem for Einstein metrics on Kahler manifolds and holomorphic vector bundles as well as its relation to the stability and degeneration phenomenon. He also investigated singular geometric structures which appeared as the limit of degeneration. Less