Isospectral compact flat manifolds

DOI10.1215/S0012-7094-92-06820-7zbMath0781.53032MaRDI QIDQ1210417

Roberto J. Miatello, Isabel Dotti Miatello

Publication date: 17 February 1994

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

holonomy groupfirst Betti numberisometry classesisospectral class

Mathematics Subject Classification ID

Finite groups of transformations in algebraic topology (including Smith theory) (55M35) Global Riemannian geometry, including pinching (53C20) Flatness and tameness of topological manifolds (57N45)

Related Items (8)

Compact flat manifolds with holonomy group 𝐙₂⊕𝐙₂ ⋮ \({\mathbb{Z}}_2^k\)-manifolds are isospectral on forms ⋮ The geometry of a bi-Lagrangian manifold ⋮ Generalized Hantzsche-Wendt flat manifolds. ⋮ Quaternion Kähler flat manifolds ⋮ The spectrum of twisted Dirac operators on compact flat manifolds ⋮ Compact flat manifolds with holonomy group \(\mathbb Z_2\oplus\mathbb Z_2\). II ⋮ Flat manifolds isospectral on \(p\)-forms.

Cites Work

• Unnamed Item
• On the holonomy group of locally euclidean spaces
• Ein Beispiel positiv definiter quadratischer Formen der Dimension 4 mit gleichen Darstellungszahlen. (An example of positive definite quadratic forms of dimension 4 with the same representation numbers)
• Riemannian coverings and isospectral manifolds
• Minimal dimensions for flat manifolds with prescribed holonomy
• Spectrum of a compact flat manifold
• Manifolds with holonomy group \(Z_2\oplus Z_2\) and first Betti number zero
• Positive definite quadratic forms with the same representation numbers
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS

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