Differential geomtery of manifold with special holonomy and their calibrated submanifolds

特殊完整流形的微分几何及其标定子流形

• 批准号: 371990-2009
• 负责人: Karigiannis, Spiro
• 金额: $ 1.68万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503684
• 关键词: Differential; geomtery; manifold; special; holonomy

My research program is in differential geometry, an area of pure mathematics which studies the existence and properties of certain kinds of geometric shapes in high dimensions. Current theories of physics for very small distances and large energies (superstring theory and supergravity) require for their description some geometric shapes of dimensions 7 and 8, possessing special properties related to their curvature. These objects have also been of independent mathematical interest, because they are closely related to some strange exceptions that arise in algebra. The goal is to study the possible types of geometric shapes that can exist with these special curvature properties. This will contribute to a better understanding of the physical theories and the beautiful mathematics which is needed to describe them.

我的研究项目是微分几何，这是纯数学的一个领域，研究高维中某些几何形状的存在和性质。当前针对极短距离和大能量的物理理论（超弦理论和超引力）需要描述一些 7 维和 8 维的几何形状，这些几何形状具有与其曲率相关的特殊性质。这些对象也具有独立的数学兴趣，因为它们与代数中出现的一些奇怪的例外密切相关。目标是研究具有这些特殊曲率特性的可能存在的几何形状类型。这将有助于更好地理解物理理论和描述它们所需的美丽数学。