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Embeddings from noncompact symmetric spaces to their compact duals
Asian Journal of Mathematics ( IF 0.6 ) Pub Date : 2020-10-01 , DOI: 10.4310/ajm.2020.v24.n5.a3
Yunxia Chen 1 , Yongdong Huang 2 , Naichung Conan Leung 3
Affiliation  

Every compact symmetric space $M$ admits a dual noncompact symmetric space $\breve{M}$. When $M$ is a generalized Grassmannian, we can view $\breve{M}$ as an open submanifold of it, consisting of space-like subspaces [4]. Motivated from this, we study the embeddings from noncompact symmetric spaces to their compact duals, including space-like embedding for generalized Grassmannians, Borel embedding for Hermitian symmetric spaces and the generalized embedding for symmetric $\mathrm{R}$‑spaces. We will compare these embeddings and describe their images using cut loci.

中文翻译:

从非紧对称空间到紧对偶的嵌入

每个紧凑的对称空间$ M $都允许有两个非紧凑的对称空间$ \ breve {M} $。当$ M $是广义的Grassmannian时,我们可以将$ \ breve {M} $视为它的一个开放子流形,它由类似空间的子空间组成[4]。因此,我们研究了从非紧致对称空间到紧对偶的嵌入,包括广义Grassmannian的空间类嵌入,埃尔米特对称空间的Borel嵌入以及对称$ \ mathrm {R} $-spaces的广义嵌入。我们将比较这些嵌入并使用切位点描述它们的图像。
更新日期:2020-10-01
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