Mathematical Sciences: Problems in Kahler and Quaternionic Kahler Geometry

数学科学：卡勒和四元数卡勒几何问题

• 批准号: 9626136
• 负责人: Kevin Corlette
• 金额: $ 10.8万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626136&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Kahler; Quaternionic

9626136 Corlette This proposal lies in the area of Kahler geometry. The geometry of a quotient space of the group of diffeomorphisms of the circle will be studied; minimal Lagrangian surfaces in complex projective and quaternionic spaces will be studied; the topology of geometrically finite quaternionic and Cayley hyperbolic manifolds will be also be investigated. Kahler geometry is the study of complex (sub-) manifolds equipped with a Kahler metric. A complex manifold is a curved space which looks locally like a complex number space; a Kahler metric then defines a distance function on the manifold compatible with its complex structure. It should be mentioned that many difficult calculations are possible only with the introduction of a complex strucure; a Kahler structure makes it possible to interpret these calculations geometrically. This is a very active area within the field of differential geometry with applications to parts of modern physics.

小行星9626136 这一建议是在该地区的卡勒几何。几何的商空间的一组同胚的圆将被研究;最小拉格朗日曲面在复杂的射影和四元数空间将被研究;拓扑的几何有限四元数和凯莱双曲流形也将被调查。 Kahler几何是研究配备Kahler度量的复（子）流形。复流形是一个局部看起来像复数空间的弯曲空间;卡勒度量定义了流形上与其复结构相容的距离函数。应该提到的是，许多困难的计算是可能的，只有通过引入一个复杂的结构;卡勒结构使得有可能解释这些计算几何。这是一个非常活跃的领域内的微分几何领域的应用部分现代物理学。