Applications of geometry of symmetric spaces to submanifold theory

一个对称空间是一个黎曼流形，它在每一点上都具有测地线对称性，这是微分几何中一个重要的和基本的对象。主要研究者证明，在联合工作与田崎博之，交叉的两个真实的形式在埃尔米特对称空间M的紧凑型是一个对映集M不一定是不可约的。她还证明，在联合工作与彼得夸斯特，任何反射子流形在对称R-空间是凸的。她还证明了，在联合工作与约斯特-辛里奇Schenburg和Quast，任何等距的半单厄米对称空间M可以扩展到线性等距的李代数G时，M是实现为伴随轨道的半单李群G。

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.