arXiv subjects

José-Manuel Fernández-Barroso

Publications and source records attributed to José-Manuel Fernández-Barroso.

2 recordsLinked to original sources

arXiv2025

Non-compact inaudibility of Naturally Reductive property

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.

math.DG↗

arXiv2025

Inaudibility of naturally reductive property

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.

math.DG↗