2025/01/21 by Vicente Cortés, Cortés, Vicente, Alejandro Gil-García +3
Mathematics · Physics and Astronomy · #53C25 #53C26 #53C40 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2501.12225
openalex publication_date 2025/01/21 · openalex created_date 2025/01/24 · openalex updated_date 2026/07/30
This paper is concerned with the geometry of principal orbits in quaternionic Kähler manifolds M of cohomogeneity one. We focus on the complete cohomogeneity one examples obtained from the non-compact quaternionic Kähler symmetric spaces associated with the simple Lie groups of type A by the one-loop deformation. We prove that for zero deformation parameter the principal orbits form a fibration by solvsolitons (nilsolitons if 4n=dim M=4). The underlying solvable group is non-unimodular if n>1 and is the Heisenberg group if n=1. We show that under the deformation, the hypersurfaces remain solvmanifolds but cease to be Ricci solitons.