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A. Loi, Filippo Salis, F. Zuddas (2019)
A characterization of complex space forms via Laplace operatorsAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 90
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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 Kähler manifolds satisfying the Δ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Delta $$\end{document}-property, i.e. such that on a neighborhood of each of its points the k-th power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k. In particular they conjectured that if a Kähler manifold satisfies the Δ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Delta $$\end{document}-property then it is a complex space form. This paper is dedicated to the proof of the validity of this conjecture.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Apr 1, 2021
Keywords: Kähler manifolds; Hermitian symmetric spaces; Kähler Laplacian; 32M15; 32Q15; 35J05
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