Remarks on the Metric Induced by the Robin Function III

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