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<p>In this paper, we use a characterization of naturally reductive 2-step nilponent Lie groups via Ambrose–Singer’s homogeneous structures to prove that one cannot determine if a closed Riemannian manifold is naturally reductive using the information encoded in the spectrum of the Laplace–Beltrami operator. To do that, we consider a new isospectral pair of 2-step nilmanifolds of dimension 9 such that one of them is naturally reductive and the other is not.</p>

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Inaudibility of naturally reductive property

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月17日

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  • Teresa Arias-Marco,
  • José-Manuel Fernández-Barroso

摘要

In this paper, we use a characterization of naturally reductive 2-step nilponent Lie groups via Ambrose–Singer’s homogeneous structures to prove that one cannot determine if a closed Riemannian manifold is naturally reductive using the information encoded in the spectrum of the Laplace–Beltrami operator. To do that, we consider a new isospectral pair of 2-step nilmanifolds of dimension 9 such that one of them is naturally reductive and the other is not.