Deformation and rigidity results for the 2k-Ricci tensor and the   2k-Gauss-Bonnet curvature
  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. 
Tiago Ca\'ula, Levi Lopes de Lima, Newton Luis Santos
math.DG