A PRODUCT MODEL FOR GENERALIZING POINCARÉ-TYPE KÄHLER METRICS

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.