Mathematical Sciences: Harmonic Maps, Kahler Manifolds and Hermitian Locally Symmetric Spaces

首席研究员将研究紧致黎曼流形上的调和映射，该流形是Kahler或黎曼局部对称的。他将尝试获得新博赫纳 身份证明几何在最优刚性定理 商的黎曼对称阀组级别大于 一个。他的方法不同于研究领域的标准方法，因为他不要求所考虑的流形被有界对称域所包围。该奖项将支持微分几何和全局分析领域的研究。微分几何是研究空间几何与空间上定义的解析概念之间关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。

The principal investigator will study harmonic maps on a compact Riemannian manifold which is either Kahler or Riemannian locally symmetric. He will attempt to obtain new Bochner identities to prove geometric rigidity theorems in optimal for quotients of Riemannian symmetric manifolds of rank greater than one. His methods are different than standard methods in the line of research since he does not require that the manifolds under consideration be folliated by bounded symmetric domains. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.