2016/10/31 by Shin-young Kim
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Combinatorics #Deformation theory #Fano plane #Homogeneous #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Rigidity (electromagnetism) #math.AG #math.DG #msc:14J45 #msc:32M12 #msc:53A55
paper · pdf · doi:10.1007/s00031-017-9415-z
published as Transformation Groups (2017) 22: 361 · 32 pages
arxiv created 2016/11/05 · openalex publication_date 2017/01/10 · arxiv updated 2017/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to quasihomogeneous varieties, we first study horospherical varieties and geometric structures modeled on horospherical varieties. Using Cartan geometry, we prove that a geometric structure modeled on a smooth projective horospherical variety of Picard number one is locally equivalent to the standard geometric structure when the geometric structure is defined on a Fano manifold of Picard number one.