Characterization of simply connected complex space forms in terms of Bergman functions

Abstract

It is well known that the Bergman functions of simply connected complex space forms (M,ω) of complex dimension n are constants ∏j=1n(m+λj)(λ≤0orλ=1k) on M for all m>m0. Conversely, this paper, under certain conditions, obtain that simply connected complete Kähler manifolds whose Bergman functions are constants ∏j=1n(m+λj)(λ≤0orλ=1) on M for all m>m0 must be holomorphically isometric to the complex space forms.