2009/09/05 by Gideon Maschler, Maschler, Gideon, Christina W. Tønnesen-Friedman +1
Mathematics · Medicine · #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Pelvic and Acetabular Injuries
paper · pdf · doi:10.48550/arxiv.0909.1060
openalex publication_date 2009/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that an admissible manifold (as defined by Apostolov, Calderbank, Gauduchon and Tønnesen-Friedman), arising from a base with a local Kähler product of constant scalar curvature metrics, admits Generalized Quasi-Einstein Kähler metrics (as defined by D. Guan) in all "sufficiently small" admissible Kähler classes. We give an example where the existence of Generalized Quasi-Einstein metrics fails in some Kähler classes while not in others. We also prove an analogous existence theorem for an additional metric type, defined by the requirement that the scalar curvature is an affine combination of a Killing potential and its Laplacian.