Non-compact inaudibility of Naturally Reductive property

2025/10/27 by Arias-Marco, Teresa, Fernández-Barroso, José-Manuel
#53C25 #58J50 #58J53 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2510.23263

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.

Citations

• Non-compact inaudibility of weak symmetry and commutativity via generalized Heisenberg groups

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