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arXiv · 2502.10332

Inaudibility of naturally reductive property

Teresa Arias-Marco·José-Manuel Fernández-Barroso
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Abstract

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.

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Teresa Arias-Marco, José-Manuel Fernández-Barroso. 2025-02-14. Inaudibility of naturally reductive property. https://arxiv.org/abs/2502.10332

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