English

Non-compact inaudibility of Naturally Reductive property

Differential Geometry 2025-10-28 v1 Spectral Theory

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.

Keywords

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)