Applications of geometry of symmetric spaces to submanifold theory

对称空间是一个黎曼流形，它在每个点上都具有测地对称性，这是微分几何中的一个重要而基本的对象。主要研究人员在与Tasaki Hiroyuki Tasaki的合作中证明了紧型Hermitian对称空间M中两个实型的交集是对脚集，其中M不一定是不可约的。在与Peter Quast的合作中，她还证明了对称R-空间中的任何反射子流形都是凸的。在与Jost-Hinrich Eschenburg和Quast的共同工作中，她还证明了当M实现为半单李群G的伴随轨道时，半单厄米特对称空间M的任一等距可推广到G的李代数的线性等距。

A symmetric space is a Riemannian manifold which admits the geodesic symmetry at each point, which is an important and fundamental object in differential geometry. The principal investigator proved, in the joint work with Hiroyuki Tasaki, that the intersection of two real forms in a Hermitian symmetric space M of compact type is an antipodal set where M is not necessarily irreducible. She also proved, in the joint work with Peter Quast, that any reflective submanifold in a symmetric R-space is convex. And she also proved, in the joint work with Jost-Hinrich Eschenburg and Quast, that any isometry of a semisimple Hermitian symmetric space M can be extended to a linear isometry of the Lie algebra of G when M is realized as an adjoint orbit of a semisimple Lie group G.