(Z₂^k)-manifolds are isospectral on forms

2004/08/20 by Roberto J. Miatello, R. J. Miatello, Miatello, R. J. +6
Mathematics · #20H15 #57R15 #58J53 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory (math.SP) #math.DG #math.SP #msc:20H15 #msc:57R15 #msc:58J53

paper · pdf · doi:10.48550/arxiv.math/0408285

15 pages, 6 figures

arxiv created 2004/08/20 · openalex publication_date 2004/08/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace operator, Δ_f, acting on sections of the full exterior bundle over an arbitrary compact flat Riemannian n-manifold M with holonomy group Z₂^k, with 0

Related

• Flat Manifolds Isospectral on p-Forms
• The multiplicity of eigenvalues of the Hodge Laplacian on 5-dimensional compact manifolds
• Spectrum of generalized Hodge-Laplace operators on flat tori and round spheres
• Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below
• Lefschetz decompositions for eigenforms on a Kähler manifold