On the $$\Delta $$-property for complex space forms

Inspired by the work of Lu and Tian (Duke Math J 125:351--387, 2004), Loi et al. address in (Abh Semin Univ Hambg 90: 99-109, 2020) problem studying those Kähler manifolds satisfying \(\Delta \)-property, i.e. such that on a neighborhood each its points k-th power Laplacian is polynomial function complex Euclidean Laplacian, for all positive integer k. In particular they conjectured if manifold satisfies \)-property then it space form. This paper dedicated to proof validity this conjecture.