Some remarks on the Kobayashi–Fuks metric on strongly pseudoconvex domains

Abstract

The Ricci curvature of the Bergman metric on a bounded domain is strictly bounded above by and consequently , where is the Bergman kernel for D on the diagonal and is the Riemannian volume element of the Bergman metric on D, is the potential for a Kähler metric on D known as the Kobayashi–Fuks metric. In this note we study the localization of this metric near holomorphic peak points and also show that this metric shares several properties with the Bergman metric on strongly pseudoconvex domains.