Mathematical Sciences: Submanifold Geometry and Polar Actions

首席研究员将研究 对称空间的子流形通过极作用在 对称空间极作用是在 对称空间，使得子流形满足 正交作用。这种作用的轨道在 子流形几何和流形上的莫尔斯理论。这 工具有望在无限维中找到应用 的情况下，以及标准的有限维情况下。 对称空间，如平面或球面，是其中之一。 几何学和物理学中最重要的空间校长 研究者将研究对称空间子空间，例如 球面上的曲线主要的工具将是研究 对称空间的不变运动，例如 球体，它有一个特定的几何关系， 子空间对这组特殊运动的理解将 提供子空间本身的几何细节。//

The principal investigator will study the geometry of submanifolds of symmetric space through polar actions on the symmetric space. A polar action is an invariant group action on the symmetric space such that the submanifold meets the orbits of the action orthogonally. The orbits of such an action play a role in the submanifold geometry and in Morse theory on the manifold. This tool is expected to find application in the infinite dimensional case as well as the standard finite dimensional case. Symmetric spaces, such as the plane or the sphere, are among the most important spaces in geometry and physics. The principal investigator will study subspaces of symmetric spaces, for example a curve on the sphere. The major tool will be a study of the invariant motions of the symmetric space, such as the rotations of the sphere, which have a particular geometric relationship with the subspace. An understanding of this special set of motions will provide details about the geometry of the subspace itself.//