Non-compact inaudibility of Naturally Reductive property
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.
Cite
@article{arxiv.2510.23263,
title = {Non-compact inaudibility of Naturally Reductive property},
author = {Teresa Arias-Marco and José-Manuel Fernández-Barroso},
journal= {arXiv preprint arXiv:2510.23263},
year = {2025}
}
Comments
This is a preprint of the Work accepted for publication in Siberian Mathematical Journal, \copyright, copyright 2025, Pleiades Publishing, Ltd. (https://pleiades.online)