Mathematical Sciences: Geometrical Structures on Manifolds and Deformations of Discrete Groups

数学科学：流形的几何结构和离散群的变形

• 批准号: 8902619
• 负责人: William Goldman
• 金额: $ 12.93万
• 依托单位: University of Maryland, College Park
• 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: 1989-07-15 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902619&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometrical; Structures; Manifolds

William Goldman plans to continue his investigation into the deformation theory of discrete groups and geometric structures. This investigation is currently divided into five (closely related) topics: 1) the deformation theory of flat bundles over Kahler manifolds, and relations with symplectic geometry, 2) real projective structures on surfaces, 3) affinely flat manifolds, including flat Lorentz manifolds, 4) the deformation space of flat PSL(2,R)-bundles over surfaces, relations with (possibly singular) geometric structures, and 5) complex hyperbolic Kleinian groups. Goldman and his students have developed graphics software particularly suited to their problems to run on a SUN work- station, and more will be done along these lines also.

威廉·戈德曼计划继续研究离散群和几何结构的形变理论。目前的研究分为五个(密切相关的)主题：1)Kahler流形上平坦丛的形变理论，以及与辛几何的关系；2)曲面上的实射影结构，3)仿射平坦流形，包括平坦Lorentz流形，4)曲面上平坦PSL(2，R)-丛的变形空间，与(可能是奇异的)几何结构的关系，(5)复双曲Kleinan群。戈德曼和他的学生已经开发出了特别适合他们的问题的图形软件，可以在SUN工作站上运行，而且还将沿着这些路线做更多的工作。