Mathematical Sciences: Twistors, Complex Manifolds, and Differential Geometry

主要研究者将研究构建 复维数常数量曲率Kaehler流形 2、两种不同的方法。 其中第一个涉及一个 广义Gibbon-Hawking模型，而第二个使用 Banach空间反函数定理在Kaehler中的应用 具有余法线型点奇点的势函数。 他将 还研究了完全非紧黎曼流形的整体变形 四元数完整流形 最后，他将 研究通用曲线的全局结构， 具有自旋结构的黎曼曲面。 在这个项目中，首席研究员将分析 与扭量和弦理论有关的复流形。 这些数学理论已经被用来解释一些 亚原子粒子的行为 流形是数学的 包括规则曲线和曲面的对象作为示例。 这两个例子都是基于真实的的多个副本 号码 在这项研究中，流形是基于副本的 复数，而不是真实的数，将用于 分析几个物理学问题。

The principal investigator will study construction of constant scalar curvature Kaehler manifolds of complex dimension 2 by two different methods. The first of these involves a generalized Gibbon-Hawking ansatz, while the second uses the Banach space inverse function theorem applied to Kaehler potentials with point singularities of conormal type. He will also study global deformations of complete non-compact Riemannian manifolds with quaternionic holonomy. Lastly, he will investigate the global structure of the universal curve for Riemann surfaces with spin structure. In this project, the principal investigator will analyze complex manifolds which relate to twistor and string theory. These mathematical theories have been used to explain some of the behavior of subatomic particles. Manifolds are mathematical objects which include regular curves and surfaces as examples. Both of these examples are based on multiple copies of the real numbers. In this study, manifolds which are based on copies of the complex numbers, instead of the real numbers, will be used to analyze several questions arising from physics.