Rigidity of proper quasi-homogeneous domains in positive flag manifolds

2024/07/26 by Blandine Galiay, Galiay, Blandine · 2 citations
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2407.18747

openalex publication_date 2024/07/26 · openalex created_date 2024/09/13 · openalex updated_date 2026/07/28

Abstract

We show that, inside the Shilov boundary of any given Hermitian symmetric space of tube type, there is, up to isomorphism, only one proper domain whose action by its automorphism group is cocompact. This gives a classification of all closed proper manifolds locally modelled on such Shilov boundaries, and provides a positive answer, in the case of flag manifolds admitting a Θ-positive structure, to a rigidity question of Limbeek and Zimmer.

Cited by

• On Markowitz's pseudodistance for conformal manifolds
• Transverse groups preserving proper domains in flag manifolds

Related

• Proper quasi-homogeneous domains in flag manifolds and geometric structures
• Transverse groups preserving proper domains in flag manifolds
• Shilov boundaries determine irreducible bounded symmetric domains
• Rigidity of holomorphic maps between Shilov boundaries of type-I bounded symmetric domains
• Nonexistence of invariant rigid structures and invariant almost rigid structures