Flat manifolds isospectral on \(p\)-forms.

DOI10.1007/BF02930761zbMath1040.58014arXivmath/0303276OpenAlexW1971256875MaRDI QIDQ1608514

Roberto J. Miatello, Juan Pablo Rossetti

Publication date: 8 August 2002

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0303276

zbMATH Keywords

flat manifoldsBieberbach groupisospectral manifolds\(p\)-spectrum

Mathematics Subject Classification ID

Other geometric groups, including crystallographic groups (20H15) Isospectrality (58J53)

Related Items (14)

Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn't reveal. ⋮ The spectrum on \(p\)-forms of a lens space ⋮ Tetra and Didi, the cosmic spectral twins ⋮ Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups ⋮ Length spectra and \(p\)-spectra of compact flat manifolds ⋮ \({\mathbb{Z}}_2^k\)-manifolds are isospectral on forms ⋮ Isospectral orbifolds with different maximal isotropy orders ⋮ Representation equivalence and \(p\)-spectrum of constant curvature space forms ⋮ $\Gamma $-extensions of the spectrum of an orbifold ⋮ Spectral properties of four-dimensional compact flat manifolds ⋮ Recent results on the spectra of Lens spaces ⋮ The spectrum of twisted Dirac operators on compact flat manifolds ⋮ A Computational Study on Lens Spaces Isospectral on Forms ⋮ Lens Spaces, Isospectral on Forms but not on Functions

Cites Work

• Zeros of generalized Krawtchouk polynomials
• Riemannian manifolds isospectral on functions but not on 1-forms
• Riemannian coverings and isospectral manifolds
• Bieberbach groups and flat manifolds
• Isospectral and non-isometric Riemannian manifolds
• Isospectral compact flat manifolds
• Continuous families of isospectral metrics on simply connected manifolds
• Compact flat manifolds with holonomy group \(\mathbb Z_2\oplus\mathbb Z_2\). II
• Continuous families of Riemannian manifolds, isospectral on functions but not on 1-forms
• Comparison of twisted \(p\)-form spectra for flat manifolds with diagonal holonomy
• On integral zeros of Krawtchouk polynomials
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Cohomology of Bieberbach groups
• Isospectral deformations I: Riemannian structures on two-step nilspaces
• Isospectral Hantzsche-Wendt manifolds
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