Mathematical Sciences: CR Geometry and Several Complex Variables

数学科学：CR 几何和多个复变量

• 批准号: 8803086
• 负责人: Howard Jacobowitz
• 金额: $ 4.92万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803086&HistoricalAwards=false
• 关键词: Mathematical; Sciences; CR; Geometry; Several

Howard Jacobowitz will continue his work in Cauchy Riemann geometry and several complex variables. This an important area which involves both topological and analytic aspects of complex variable theory. Jacobowitz will bring geometric techniques to bear on the problems under investigation. A major theme throughout the research will be embedding problems for Cauchy Riemann structures. One aim of the research is to prove a more general boundary version of the Newlander-Nirenberg theorem and thereby obtain conditions for the local embeddability of more general CR structures. Another objective is to generalize an example of a locally but not globally embeddable CR structure. Jacobowitz will also continue his investigations of the prevalence of Fefferman spirals and their relations to points of zero Cartan curvature. A final topic is the study of the conformal class of certain singular two-dimensional metrics. Here he will associate with each metric a complex vector field and investigate the homogeneous solvability of the vector field.

霍华德·雅各布维茨将继续他在柯西·里曼的工作 几何和几个复杂的变量。这是一个重要的领域 它涉及复杂的拓扑和分析方面， 变量理论阿博维茨将把几何技术， 与正在调查的问题有关。一个主要主题 在整个研究过程中， Riemann结构 研究的目的之一是证明一个更一般的边界 Newlander-Nirenberg定理的一个版本，从而得到 更一般CR的局部可嵌入性条件 结构.另一个目标是推广一个例子， 局部但非全局可嵌入的CR结构。博维茨将 他还继续调查February man的流行情况， 螺线及其与Cartan曲率为零的点的关系。一 最后一个主题是研究某些 奇异二维度量在这里，他将与 每个度量都是一个复向量场，并研究 向量场的齐次可解性