Maximal Weinstein neighborhoods of symmetric R-spaces and their symplectic capacities

2025/05/05 by Johanna Bimmermann, Bimmermann, Johanna
Mathematics · #51M15 #53C35 #53D20 #53D25 #Advanced Algebra and Geometry #Advanced Banach Space Theory #FOS: Mathematics #Finite Group Theory Research #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2505.02731

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Symmetric R-spaces can be characterized as real forms of Hermitian symmetric spaces, and as such, they are all embedded as Lagrangian submanifolds. We show that their maximal Weinstein tubular neighborhoods are dense and use this property to compute both the Gromov width and the Hofer--Zehnder capacity of the corresponding disc (co)tangent bundles of the symmetric R-spaces.

Citations

• On symplectic geometry of tangent bundles of Hermitian symmetric spaces
• Hofer-Zehnder capacity of magnetic disc tangent bundles over constant curvature surfaces
• Hofer-Zehnder capacity of disc tangent bundles of projective spaces
• Uniqueness of Lagrangians in T^*RP2
• Canonical domains for coadjoint orbits
• Symplectic capacities from Hamiltonian circle actions
• Mostow's Decomposition Theorem for L*-groups and Applications to affine coadjoint orbits and stable manifolds
• Complex extensions of semisimple symmetric spaces
• Maximal Complexifications of Certain Riemannian Homogeneous Manifolds
• The Geometry of Grauert Tubes and Complexification of Symmetric Spaces

Related

• On symplectic geometry of tangent bundles of Hermitian symmetric spaces
• Higher P-symmetric Ekeland-Hofer capacities
• A lower bound for the radius of Weinstein's Lagrangian tubular neighborhood
• Generalized Weinstein tubular neighbourhood & Space of Lagrangian submersions
• Relative Hofer-Zehnder capacity and positive symplectic homology