2015/02/25 by Wafaâ Batat, Stuart James Hall, Batat, Wafaa +5
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1502.07140
openalex publication_date 2015/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the quasi-Einstein metrics found by Lü, Page and Pope on ℂP1-bundles over Fano Kähler-Einstein bases are conformally Kähler and that the Kähler class of the conformal metric is a multiple of the first Chern class. A detailed study of the lowest-dimensional example of such metrics on ℂP2\sharp ℂP2 using the methods developed by Abreu and Guillemin for studying toric Kähler metrics is given. Our methods yield, in a unified framework, proofs of the existence of the Page, Koiso-Cao and Lü-Page-Pope metrics on ℂP2\sharp ℂP2. Finally, we investigate the properties that similar quasi-Einstein metrics would have if they also exist on the toric surface ℂP2\sharp 2 ℂP2.