Einstein manifolds and related structures

爱因斯坦流形及相关结构

• 批准号: 9421-2010
• 负责人: Wang, Mckenzie
• 金额: $ 2.55万
• 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: 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=508855
• 关键词: Einstein; manifolds; related; structures

This proposal deals with the existence, moduli, and geometrical properties of solutions of a number of geometric differential equations analogous to Einstein's field equation in General Relativity. These equations make sense for spaces of all dimensions greater than two on which there is a notion of lengths and angles between tangent vectors. The equations under study are of fundamental interest in Differential Geometry because they express either the constancy of a natural notion of curvature or self-similarity for solutions to a natural flow on the space of Riemannian metrics on a given space. These equations also arise naturally in supergravity theories, in which one seeks a unification of General Relativity with theories explaining the other forces in nature.

该提案涉及许多几何微分方程的解决方案的存在，模量和几何特性，类似于一般相对论中的爱因斯坦磁场方程。这些方程对于大于两个尺寸的空间的空间很有意义，在两个方面之间存在切线向量之间的长度和角度的概念。所研究的方程在差异几何形状中具有基本兴趣，因为它们表达了自然曲率概念或自相似性的恒定性，用于在给定空间上riemannian指标空间上自然流动的解决方案。这些方程式也自然出现在超级重力理论中，在这种理论中，人们寻求与解释自然界其他力量的理论的一般相对性的统一。