Mathematical Sciences: Differential Geometry

数学科学：微分几何

• 批准号: 8701609
• 负责人: Wu-Yi Hsiang
• 金额: $ 53.06万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-05-15 至 1990-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701609&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometry

This research will cover many aspects of contemporary geometry. The geometers at Berkeley form one of the world's major centers of excellence. All four investigators have consistently made outstanding contributions to geometry and the prospects for substantial progress in the present research program are very exciting. Hsiang will continue his work in global differential geometry of submanifolds, in geometry of simplexes in constant curvature spaces and symmetric spaces and in the geometry and the topology of Lie transformation groups. Weinstein will carry out research in symplectic geometry and its relations with other areas of geometric analysis and mathematical physics. In particular he will investigate the connections between symplectic geometry and operator algebra. This is one of the most exciting areas of modern geometry and Weinstein is universally acknowledged as being at the forefront of this research. Chern is the grand old man of modern differential geometry whose continued activity into his seventies is inspiring. He will work principally on two projects. The first concerns taut immersions and Lie sphere geometry. The second continues work done with Wolfson concerning harmonic maps of a surface into classical spaces. Wu will work on harmonic maps, the geometry of 4-manifolds and rational homotopy in Riemannian geometry. This will continue his excellent work on Kaehler manifolds relating function theory with curvature properties.

这项研究将涵盖当代的许多方面， 几何伯克利的几何学家是世界上最重要的几何学家之一， 卓越中心。所有四名调查员都一直 对几何学和几何学的前景做出了杰出的贡献 目前的研究计划取得了很大进展， 令人兴奋. Hsiang将继续他在全球差分方面的工作 子流形的几何学，在常数单形的几何学中 曲率空间和对称空间，以及几何学和 李变换群的拓扑 温斯坦将开展辛几何方面的研究， 它与其他几何分析领域的关系， 数学物理特别是他将调查 辛几何和算子代数之间的联系。 这是现代几何学中最令人兴奋的领域之一， 温斯坦被公认为是 这项研究。 陈省身是现代微分几何学的鼻祖 他在七十多岁时仍继续开展活动，令人鼓舞。他将 主要做两个项目。第一个问题与taut有关 浸入和李球几何。第二个继续工作 关于曲面的调和映射到 古典空间 吴将致力于调和映射，几何的4-流形 和有理同伦。这将继续 他出色的工作凯勒流形有关的功能理论 具有曲率特性。