2020/10/07 by Jorge Lauret, Lauret, Jorge, Cynthia E. Will +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.2010.03643
31 pages. Final version to appear in Journal für die reine und angewandte Mathematik (Crelle's journal)
arxiv created 2021/10/29 · arxiv updated 2021/11/02
The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M=G/K is studied. We focus on the metrics at which the Ricci curvature map is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.