Remarks on the Metric Induced by the Robin Function III

Abstract

Let D be a smoothly bounded pseudo convex domain in Cn, n > 1. Using the Robin function A(p) that arises from the green function G(z, p) for D with pole at p E D associated with the standard sum-of-squares Laplacian, N. Levenberg and H. Yamaguchi had constructed a Kahler metric (the so-called A-metric) on D. In this article, we study the existence of geodesic spirals for this metric.