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arXiv · 2510.23263

Non-compact inaudibility of Naturally Reductive property

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

Naturally reductive manifolds are an important class of Riemannian manifolds because they provide examples that generalize the locally symmetric ones. A property is said to be inaudible if there exists a unitary operator which intertwines the Laplace-Beltrami operator of two Riemannian manifolds such that one of them satisfies the property and the other does not. In this paper, we study the relation between 2-step nilpotent Lie groups and the naturally reductive property to prove that this property is inaudible, using a pair of non-compact 11-dimensional generalized Heisenberg groups.

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Teresa Arias-Marco, José-Manuel Fernández-Barroso. 2025-10-27. Non-compact inaudibility of Naturally Reductive property. https://arxiv.org/abs/2510.23263

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