Einstein manifolds and related structures

这个建议涉及的存在性，模，和几何性质的解决方案的一些几何微分方程类似于爱因斯坦的场方程在广义相对论。这些方程对于所有大于2维的空间都是有意义的，在这些空间上有切向量之间的长度和角度的概念。研究中的方程是微分几何的根本兴趣，因为它们表达了曲率或自相似性的自然概念的恒定性，用于解决给定空间上黎曼度量空间上的自然流。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。

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.