Mathematical Sciences: Geometry of Compact Nonpositively Curved Manifolds of Rank 1

数学科学：一阶紧致非正曲流形的几何

• 批准号: 8901341
• 负责人: Patrick Eberlein
• 金额: $ 9.29万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-05-15 至 1992-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901341&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Compact; Nonpositively

The principal investigator will continue his study of the geometry of complete Riemannian manifolds of finite volume and nonpositive curvature. Particular emphasis will be given to manifolds of rank 1, a condition implied by but weaker than strictly negative sectional curvature. The research project will include the investigation of both geometric characterizations of symmetric spaces with strictly negative sectional curvature, and algebraic properties of the fundamental groups of the base manifold. Mathematicians have studied generalized surfaces, called manifolds, for more than a century. A so called "Riemannian manifold" may have a well-defined area or volume. For example, as we usually imagine them, spheres and tori have finite surface area. The principal investigator will study manifolds of nonpositive curvature. One example of such a manifold would be the two-holed torus. This line of research has been particularly active in the 1980's due in large part to earlier pioneering efforts of the principal investigator.

首席研究员将继续研究 有限体积的完备黎曼流形的几何 非正曲率 将特别重视 流形的秩1，一个条件隐含但弱于 严格负截面曲率。 该研究项目将 包括两个几何特征的调查， 具有严格负截面曲率的对称空间，以及 基的基本群的代数性质 歧管 数学家研究了广义曲面，称为 流形，超过一个世纪。 所谓的“黎曼” “歧管”可以具有明确限定的面积或体积。 比如说， 正如我们通常想象的那样，球面和环面具有有限的表面， 区 主要研究者将研究 非正曲率这种流形的一个例子是 有两个孔的环面这一系列的研究尤其 在1980年代活跃，很大程度上是由于早期的开拓性 主要研究者的努力。