Embeddings from noncompact symmetric spaces to their compact duals

2018/11/07 by Yunxia Chen, Chen, Yunxia, Yongdong Huang +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1811.02778

openalex publication_date 2018/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Every compact symmetric space M admits a dual noncompact symmetric space \checkM. When M is a generalized Grassmannian, we can view \checkM as a open submanifold of it consisting of space-like subspaces \citeHL. 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.

Related

• Kähler duality and projective embeddings
• Equivariant realizations of Hermitian symmetric space of noncompact type
• Submanifold geometry in symmetric spaces of noncompact type
• Equivariant Embeddings of Kälerian Symmetric Spaces
• A class of complete embedded minimal submanifolds in noncompact symmetric spaces