Mathematical Sciences: Homogeneous Complex Manifolds and Isoparametric Hypersurfaces in Spheres and Nonlinear PartialDifferential Equations

数学科学：齐次复流形、球体中的等参超曲面和非线性偏微分方程

• 批准号: 8705813
• 负责人: Josef Dorfmeister
• 金额: $ 2.88万
• 依托单位: University of Georgia
• 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: 1987-07-01 至 1988-08-23
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8705813&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homogeneous; Complex; Manifolds

Josef Dorfmeister will carry out research in three areas. These concern homogeneous complex manifolds, isoparametric hypersurfaces in spheres and nonlinear partial differential equations. Dorfmeister, in collaboration with Nakajima and Neher has recently achieved remarkable results concerning homogeneous Kahler manifolds and certain isoparametric triple systems. He will continue to apply algebraic and functional analytic techniques to related problems. In particular he will try to determine all Kahler structures on manifolds which admit a transitive group of automorphisms. The second major project will be to describe all Lie algebras which occur as infinitesimal automorphisms of some homogeneous Kahler manifold. The final part of the program concerns an investigation of the class of contractible, rational, homogeneous domains in complex n-dimensional space.

Josef Dorfmeister将在三个领域开展研究。 这些涉及齐次复流形，等参 球面超曲面与非线性偏微分 方程 Dorfmeister与Nakajima和Neher合作， 最近取得了显着成果，关于均匀 Kahler流形与某些等参三元系。他 将继续应用代数和泛函分析 相关问题的技术。特别是，他将努力 确定流形上的所有Kahler结构， 自同构的传递群第二大项目将 描述所有作为无穷小出现的李代数 一些齐次Kahler流形的自同构最后一部分 该计划涉及的一类调查， 复域中的可收缩、有理、齐次域 n维空间