Riemannian Geometry

黎曼几何

• 批准号: 7873-2006
• 负责人: MinOo, Maung
• 金额: $ 0.95万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=362252
• 关键词: Riemannian; Geometry

Geometry is one of the oldest disciplines in Science and curvature is the fundamental invariant of Geometry. The basic problem is to understand the relation between curvature and the global shape of space. These ideas are closely intertwined with fundamental questions in theoretical physics. One of the objectives is to study and classify spaces with optimal curvature. Well known examples, which play an important role in contemporary high-energy physics, are Einstein metrics, Yang-Mills connections and metrics of special holonomy such as Calabi-Yau spaces. The main goal of this research proposal is to probe deeper into the geometric properties of these higher dimensional spaces with special curvature, using methods of analysis and insights from physics. I also plan to apply geometric ideas to areas such as probability and statistics.

几何是科学中最古老的学科之一，曲率是几何的基本不变量。基本问题是理解曲率与空间整体形状之间的关系。这些想法与理论物理学的基本问题密切相关。目标之一是研究和分类具有最佳曲率的空间。在当代高能物理学中发挥着重要作用的众所周知的例子是爱因斯坦度量、杨-米尔斯联系和特殊完整度量（例如卡拉比-丘空间）。本研究计划的主要目标是利用分析方法和物理学见解，更深入地探讨这些具有特殊曲率的高维空间的几何特性。我还计划将几何思想应用到概率和统计等领域。