2015/04/30 by Artem Pulemotov · 23 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Combinatorics #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Homogeneous #Invariant (physics) #Lie group #Mathematical physics #Mathematics #Pure mathematics #Ricci curvature #Riemann curvature tensor #Symmetric space #math.AP #math.DG
paper · pdf · doi:10.1016/j.geomphys.2016.04.003
published in Journal of Geometry and Physics 106, 275-283 (Elsevier BV) · 11 pages
arxiv created 2016/04/15 · openalex publication_date 2016/04/28 · arxiv updated 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let G be a compact connected Lie group and H a closed subgroup of G. Suppose the homogeneous space G/H is effective and has dimension 3 or higher. Consider a G-invariant, symmetric, positive-semidefinite, nonzero (0,2)-tensor field T on G/H. Assume that H is a maximal connected Lie subgroup of G. We prove the existence of a G-invariant Riemannian metric g and a positive number c such that the Ricci curvature of g coincides with cT on G/H. Afterwards, we examine what happens when the maximality hypothesis fails to hold.