On the boundary behavior of the holomorphic sectional curvature of the Bergman metric

We obtain a conceptually new differential geometric proof of P. F. Klembeck's result (cf. [9]) that the holomorphic sectional curvature $k_g(z)$ of the Bergman metric of a strictly pseudoconvex domain $\Omega \subset \mathbb{C}^n approaches $-4/(n+1)$ (the constant sectional curvature of the Bergman metric of the unit ball) as $z \to \partial \Omega$.