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

TL;DR

This paper studies how the Kobayashi--Fuks metric and related invariants behave near the boundary of strictly pseudoconvex domains, using scaling techniques to extend and refine previous analyses.

Contribution

It provides a detailed boundary analysis of the Kobayashi--Fuks metric and associated invariants, including curvature and canonical invariants, in strictly pseudoconvex domains.

Findings

Boundary behavior of the Kobayashi--Fuks metric is characterized.

Invariants like holomorphic sectional curvature are analyzed near the boundary.

Refined understanding of invariant properties in complex analysis 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.