2021/11/30 by Ethan L Addison, Addison, Ethan L
Mathematics · #32Q15 (Secondary) #53C55 (Primary) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2112.00097
openalex publication_date 2021/11/30 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We begin by defining a type of Kähler metric near the zero section of a trivial holomorphic open disk bundle N over a compact Kähler manifold X by incorporating flows generated by holomorphic vector fields on X. These metrics are then shown to deviate exponentially from Poincaré-type metrics on N∖ X in terms of the log-polar distance from X in N. Lastly we see that they arise naturally when perturbing classes containing Poincaré-type Kähler metrics of constant scalar curvature to obtain nearby cscK metrics even when the perturbed class on X does not admit a cscK metric.