Mathematical Sciences: Topics in Riemannian and Complex Geometry

数学科学：黎曼和复几何主题

• 批准号: 9505744
• 负责人: Michael Anderson
• 金额: $ 15万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505744&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Riemannian; Complex

9505744 Anderson The proposed research covers two areas, Riemannian geometry and complex differential geometry. It is proposed to classify compact Riemannian manifolds which are extrema of the quadratic Riemmanian functional. In addition, quaternionic Kahler manifolds and extremal Kahler metrics are to be investigated. Riemannian manifolds are higher dimensional generalizations of curved surfaces. They are abstract objects in that they exist on their own rather than in an ambient space. Kahler manifolds are complex analogs of Riemannian manifolds: just as the study of complex functions provides insights into real functions, the study of Kahler manifolds often reveal unexpected features of Riemannain manifolds.

9505744 Anderson 提议的研究涵盖两个领域，黎曼几何和复微分几何。提出对二次黎曼泛函的极值紧黎曼流形进行分类。此外，还将研究四元数卡勒流形和极值卡勒度量。 黎曼流形是曲面的高维推广。它们是抽象对象，因为它们独立存在，而不是存在于周围空间中。卡勒流形是黎曼流形的复数类似物：正如复函数的研究提供了对实函数的见解一样，卡勒流形的研究也经常揭示黎曼流形的意想不到的特征。