The inaudible geometry of nilmanifolds

DOI10.1007/BF01231288zbMath0779.53026OpenAlexW1981645275MaRDI QIDQ2366469

Carolyn S. Gordon, Herman Gluck, David L. Webb, Dennis M. DeTurck

Publication date: 29 June 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144078

zbMATH Keywords

geodesicsisospectral deformationsLaplace spectrumDrifting Subspaces

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20)

Related Items

Volume-minimizing cycles in Grassmann manifolds ⋮ Lax-type isospectral deformations on nilmanifolds ⋮ The geometry of filiform nilpotent Lie groups ⋮ Geometry of $2$-step nilpotent groups with a left invariant metric ⋮ The stable 4-dimensional geometry of the real Grassmann manifolds ⋮ Horizontal submanifolds of groups of Heisenberg type ⋮ Line bundle Laplacians over isospectral nilmanifolds ⋮ Continuous families of Riemannian manifolds, isospectral on functions but not on 1-forms

Cites Work

• You can not hear the mass of a homology class
• Isospectral deformations of compact solvmanifolds
• Calibrated geometries
• Normal and integral currents
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• Isospectral deformations II: Trace formulas, metrics, and potentials
• Constructing Isospectral Manifolds
• The stable homology of flat torus.
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