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<p>Naturally reductive manifolds form an important class of Riemannian manifolds because they provide examples that generalize locally symmetric ones.A property is said to be inaudible if there exists a unitary operator intertwining the Laplace–Beltrami operators of two Riemannian manifolds such that one of them enjoys the property whereas the other does not.In this paper we study the relation between <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ 2 $</EquationSource> </InlineEquation>-step nilpotent Lie groups and the naturally reductive property and prove that this property is inaudible by using a pair of noncompact <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ 11 $</EquationSource> </InlineEquation>-dimensional generalized Heisenberg groups.</p>

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Noncompact Inaudibility of the Naturally Reductive Property

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月28日

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  • T. Arias-Marco,
  • J.-M. Fernández-Barroso

摘要

Naturally reductive manifolds form an important class of Riemannian manifolds because they provide examples that generalize locally symmetric ones.A property is said to be inaudible if there exists a unitary operator intertwining the Laplace–Beltrami operators of two Riemannian manifolds such that one of them enjoys the property whereas the other does not.In this paper we study the relation between $ 2 $ -step nilpotent Lie groups and the naturally reductive property and prove that this property is inaudible by using a pair of noncompact $ 11 $ -dimensional generalized Heisenberg groups.