Mathematical Sciences: Manifolds of Nonpositive Curvature, Two-point Homogeneous Spaces and Blaschke Manifolds

首席研究员将研究两个问题， 非正曲率流形以及两个问题 包括齐性空间和Blaschke流形。 更 具体地，这些问题涉及到 的几何测度论特征 阿达玛流形，特征值的恒定性，和Blaschke 流形，其完整群是例外的。 双孔内胎的表面是一个示例， 可能有非正曲率的流形。 这些有他们的 更高维度的类似物 其中一个的叶理是 低维表面的集合堆叠在一起， 填满歧管。 holonomy群是一个度量 当他们扫过他们的叶子时， 环境歧管。 首席研究员将深入研究 关于特殊种类流形上的完整性的问题。

The principal investigator will study two problems in manifolds of nonpositive curvature as well as two problems involving homogeneous spaces and Blaschke manifolds. More specifically these problems concern the symmetry of solvmanifolds, geometric measure theoretic characterizations of Hadamard manifolds, constancy of eigenvalues, and Blaschke manifolds whose holonomy group is exceptional. The surface of a two-holed inner tube is an example of a manifold which may have nonpositive curvature. These have their higher-dimensional analogues. A foliation of one of these is a collection of lower-dimensional surfaces stacked together which fill up the manifold. The holonomy group is a measure of the twisting and shearing of such leaves as they sweep through their ambient manifolds. The principal investigator will study deep questions concerning holonomy on specialized sorts of manifolds.