Mathematical Sciences: Geometry and Analysis on CR Manifolds

数学科学：CR 流形的几何与分析

• 批准号: 8702618
• 负责人: John Lee
• 金额: $ 3.36万
• 依托单位: University of Washington
• 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: 1987-07-15 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702618&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Analysis; CR

John Lee will continue his studies of Cauchy Riemann manifolds. He will investigate the ways in which certain curvature and torsion tensors on a pseudohermitian manifold can be simplified by appropriate choice of CR structure and contact form. The principal problems to be considered are 1) the CR Yamabe problem which asks for a contact form with constant scalar curvature; 2) to choose a contact form for which the Webster Ricci tensor is a scalar multiple of the Levi form; 3) to determine which CR manifolds admit contact forms satisfying both previous conditions; 4) to determine conditions under cwhich the CR structure can be varied to achieve vanishing torsion and constant scalar curvature.

约翰·李将继续研究柯西·黎曼流形。他将研究如何通过适当选择CR结构和接触形式来简化伪厄米特流形上的某些曲率张量和扭转张量。要考虑的主要问题是：1)CR Yamabe问题，它要求具有常数量曲率的接触形式；2)选择Webster Ricci张量是Levi形式的标量倍数的接触形式；3)确定哪些CR流形允许满足上述两个条件的接触形式；4)确定可以改变CR结构以实现零扭转和恒定标量曲率的条件。