Inaudibility of naturally reductive property

2025/02/14 by Arias-Marco, Teresa, Fernández-Barroso, José-Manuel
#53C25 #53C30 #58J50 #58J53 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2502.10332

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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