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arXiv · 2010.16075

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

Roberto Mossa
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Abstract

Inspired by the work of Z. Lu and G. Tian [8], A. Loi, F. Salis and F. Zuddas address in [5] the problem of studying those K\"ahler manifolds satisfying the $\Delta$-property, i.e. such that on a neighborhood of each of its points the $k$-th power of the K\"ahler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer $k$. In particular, they conjectured that if a K\"ahler 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.

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Roberto Mossa. 2020-10-29. On the $\Delta$-property for complex space forms. https://doi.org/10.1007/s12188-021-00233-3

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