On the Boundary Behaviour of Invariants and Curvatures of the Kobayashi--Fuks Metric in Strictly Pseudoconvex Domains

Abstract

The purpose of this article is to investigate the boundary behaviour of the Kobayashi--Fuks metric and several associated invariants on strictly pseudoconvex domains in the paradigm of scaling. This approach allows us to examine more invariants, such as the canonical invariant, holomorphic sectional curvature, and Ricci curvature of this metric, in a manner that extends and refines some existing analysis.