On the Δ-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 Math Semin Univ Hambg 90: 99-109, 2020) the problem of studying those Kahler manifolds satisfying the Delta-property, i.e. such that on a neighborhood of each of its points the k-th power of the Kahler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k. In particular they conjectured that if a Kahler manifold satisfies the Delta-property then it is a complex space form. This paper is dedicated to the proof of the validity of this conjecture.

Automated summary

This paper explores the property of Kahler manifolds satisfying the Delta-property, showing that manifolds with this property are complex space forms.