Local symmetry of harmonic spaces as determined by the spectra of small geodesic spheres

DOI10.1007/s00039-012-0146-yzbMath1246.53050arXiv1001.1611OpenAlexW2962828584MaRDI QIDQ412044

Dorothee Schueth, Teresa Arias-Marco

Publication date: 3 May 2012

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1611

zbMATH Keywords

second fundamental formgeodesic spheresheat invariantscurvature invariantsgeodesic ballsDamek-Ricci spacesharmonic spaceisospectral manifoldsLedger's recursion formula

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Nilpotent and solvable Lie groups (22E25) Global Riemannian geometry, including pinching (53C20) Isospectrality (58J53)

Related Items (4)

The angular Laplacian on symmetric Damek-Ricci spaces ⋮ Harmonic manifolds of hypergeometric type and spherical Fourier transform ⋮ Full Laplace spectrum of distance spheres in symmetric spaces of rank one ⋮ The biradial Paley-Wiener theorem for the Helgason Fourier transform on Damek-Ricci spaces

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