SEARCH

SEARCH BY CITATION

Keywords:

  • 2k-Ricci tensor;
  • 2k-Gauss-Bonnet curvature;
  • deformation;
  • rigidity;
  • double forms;
  • Yamabe problem;
  • Primary: 53C25;
  • Secondary: 58J05

We present several deformation and rigidity results within the classes of closed Riemannian manifolds which either are 2k-Einstein (in the sense that their 2k-Ricci tensor is constant) or have constant 2k-Gauss-Bonnet curvature. The results hold for a family of manifolds containing all non-flat space forms and the main ingredients in the proofs are explicit formulae for the linearizations of the above invariants obtained by means of the formalism of double forms.