Isospectral metrics and potentials on classical compact simple Lie groups

2004/08/11 by Emily Proctor, Proctor, Emily
Mathematics · Physics and Astronomy · #58J53 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0408152

openalex publication_date 2004/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of multiparameter isospectral deformations of metrics on SO(n) (n = 9 and n≥ 11), SU(n) (n≥ 8), and Sp(n) (n≥ 4). For these examples, we follow a metric construction developed by Schueth who had given one-parameter families of isospectral metrics on orthogonal and unitary groups. Our multiparameter families are obtained by a new proof of nontriviality establishing a generic condition for nonisometry of metrics arising from the construction. We also show the existence of non-congruent pairs of isospectral potentials and nonisometric pairs of isospectral conformally equivalent metrics on Sp(n) for n≥ 6.

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