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<p>We prove that the spectrum of the Kohn Laplacian does not determine the equivalence classes of CR manifolds. We construct pairs of odd-dimensional elliptic manifolds that are not equivalent as CR manifolds but whose Kohn Laplacians have the same spectrum. These manifolds are endowed with the CR structures inherited from the canonical CR structure on the sphere of the same dimension. We provide three different constructions among lens spaces and an additional one among elliptic manifolds with non-cyclic fundamental groups.</p>

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Isospectral CR Manifolds with Respect to the Kohn Laplacian

  • 期刊论文

  • 发表日期：

    2025年4月16日

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  • Gerson Gutierrez,
  • Emilio A. Lauret,
  • Juan Pablo Rossetti

摘要

We prove that the spectrum of the Kohn Laplacian does not determine the equivalence classes of CR manifolds. We construct pairs of odd-dimensional elliptic manifolds that are not equivalent as CR manifolds but whose Kohn Laplacians have the same spectrum. These manifolds are endowed with the CR structures inherited from the canonical CR structure on the sphere of the same dimension. We provide three different constructions among lens spaces and an additional one among elliptic manifolds with non-cyclic fundamental groups.