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

The Ricci curvature of the Bergman metric on a bounded domain $D\subset \mathbb{C}^n$ is strictly above by $n+1$ and consequently $\log (K_D^{n+1}g_{B,D})$, where $K_D$ kernel for $D$ diagonal $g_{B, D}$ Riemannian volume element $D$, potential K\"ahler known as Kobayashi--Fuks metric. In this note we study localization near holomorphic peak points also show that shares several properties with strongly pseudoconvex domains.