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

Abstract

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 Ω ⊂ ℂ n approaches −4/(n + 1) (the constant sectional curvature of the Bergman metric of the unit ball) as z → ∂ Ω.