Embeddings from noncompact symmetric spaces to their compact duals

Yunxia Chen; Yongdong Huang; Naichung Conan Leung

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arXiv · 1811.02778

Embeddings from noncompact symmetric spaces to their compact duals

Yunxia Chen·Yongdong Huang·Naichung Conan Leung

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Abstract

Every compact symmetric space $M$ admits a dual noncompact symmetric space $\check{M}$. When $M$ is a generalized Grassmannian, we can view $\check{M}$ as a open submanifold of it consisting of space-like subspaces \cite{HL}. 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 R-spaces. We will compare these embeddings and describe their images using cut loci.

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BibTeX RIS

Yunxia Chen, Yongdong Huang, Naichung Conan Leung. 2018-11-07. Embeddings from noncompact symmetric spaces to their compact duals. https://arxiv.org/abs/1811.02778

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