Automorphisms of generic gradient vector fields with prescribed finite symmetries

• Ignasi Mundet i Riera ^[1]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 5, 2019, págs. 1281-1308
• Idioma: inglés
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• Resumen

  • Let M be a compact and connected smooth manifold endowed with a smooth action of a finite group Γ, and let f be a Γ-invariant Morse function on M. We prove that the space of Γ-invariant Riemannian metrics on M contains a residual subset Metf with the following property. Let g∈Metf and let ∇gf be the gradient vector field of f with respect to g. For any diffeomorphism ϕ∈Diff(M) preserving ∇gf there exists some t∈R and some γ∈Γ such that for every x∈M we have ϕ(x)=γΦgt(x), where Φgt is the time-t flow of the vector field ∇gf.