Mathematical Sciences: Differential Geometry and Geometric Analysis

三名研究人员将研究涉及 非负曲流形的结构，测地线，极小 真实的Kaehler子流形，有界曲率的坍缩， 拉普拉斯算子的绝热极限和小特征值，以及 黎曼流形和半单流形的刚性性质 组 这些研究人员将分析的各个方面， 理解所有弯曲流形的问题。 这个一般 问题一直是微分几何的中心主题，因为 一百多年前的构想。 具体来说，这些 研究人员将研究测地线沿着曲线的行为 流形 在球面上，大圆是 只有测地线。 但在其他更复杂的表面上，测地线 可以呈现出许多令人惊讶的特性。 测地线学对测地线的研究 对宇宙学有特殊的应用， 根据爱因斯坦的理论，我们每个人都在四维空间中移动 时空沿着测地线。

Three investigators will study problems involving the structure of non-negatively curved manifolds, geodesics, minimal real Kaehler submanifolds, collapse with bounded curvature, adiabatic limits and small eigenvalues of the Laplacian, and rigidity properties of Riemannian manifolds and semisimple groups. These investigators will analyze various aspects of the problem of understanding all curved manifolds. This general problem has been the central theme of differential geometry since its conception over one hundered years ago. Specifically, these investigators will study the behavior of geodesics along curved manifolds. On the surface of a sphere, great circles are the only geodesics. But on other more complex surfaces, geodesics can take on many surprising properties. The study of geodesics has particular application to cosmology since according to Einstein's theories, each of us moves through four-dimensional space-time along a geodesic.