Applications of geometry of symmetric spaces to submanifold theory

对称空间是每一点都具有测地线对称性的黎曼流形，是微分几何中一个重要而基本的对象。在与Hiroyuki Tasaki的联合研究中，证明了紧型埃尔密对称空间M中两实形式的交集是一个对映集，其中M不一定是不可约的。在与Peter Quast的联合工作中，她还证明了对称r空间中的任何反射子流形都是凸的。她还在与Jost-Hinrich Eschenburg和Quast的联合工作中证明，当M被实现为半单李群G的伴随轨道时，半单厄米对称空间M的任何等距都可以推广到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.