Homogeneous quaternionic Kaehler structures and quaternionic hyperbolic space

2005/04/27 by Marco Castrillón López, M. Castrillon Lopez, P. M. Gadea +5
Mathematics · Physics and Astronomy · #53C26 #53C30 #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #math.DG #msc:53C26 #msc:53C30

paper · pdf · doi:10.48550/arxiv.math/0504550

40 pages

arxiv created 2005/04/27 · openalex publication_date 2005/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is characterised by admitting homogeneous structures of a particularly simple type. In the process we study the properties of different homogeneous models for HH(n).

Related

• Non-degenerate homogeneous ε-Kähler and ε-quaternion Kähler structures of linear type
• Hyper-Hermitian quaternionic Kaehler manifolds
• Homogeneous structures of linear type on ε-Kähler and ε-quaternion Kähler manifolds
• The homogeneous geometries of real hyperbolic space
• Classification of indefinite hyper-Kaehler symmetric spaces