Spectrally distinguishing symmetric spaces II

• Emilio A. Lauret ^[1] ; Juan S. Rodrı́guez ^[2]
  1. [1] Universidad Nacional del Sur

     Universidad Nacional del Sur

     Argentina

     
  2. [2] Pontífica Universidad Javeriana

     Pontífica Universidad Javeriana

     Colombia

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 40, Nº 1, 2025, págs. 91-120
• Idioma: inglés
• DOI: 10.17398/2605-5686.40.1.91
• Enlaces
  • Texto completo (pdf)
• Resumen

  • The action of the subgroup G2 of SO(7) (resp. Spin(7) of SO(8)) on the Grassmannian space M = SO(7)/(SO(5)×SO(2)) (resp. M = SO(8)/(SO(5)×SO(3)) ) is still transitive. We prove that the spectrum (i.e. the collection of eigenvalues of its Laplace-Beltrami operator) of a symmetric metric g0 on M coincides with the spectrum of a G2-invariant (resp. Spin(7)-invariant) metric g on M only if g0 and g are isometric. As a consequence, each non-flat compact irreducible symmetric space of non-group type is spectrally unique among the family of all currently known homogeneous metrics on its underlying differentiable manifold.

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