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.

这一建议涉及一些几何微分方程解的存在性、模和几何性质，类似于广义相对论中的爱因斯坦场方程解。这些方程对于所有维度大于2的空间都有意义，在这些空间上存在切线向量之间的长度和角度的概念。所研究的方程是微分几何中的基本兴趣，因为它们要么表示自然曲率概念的不变性，要么表示给定空间上黎曼度量空间上的自然流的解的自相似性。这些方程也自然地出现在超引力理论中，在超引力理论中，人们寻求广义相对论与解释自然界中其他力的理论的统一。