Deformation and rigidity results for the 2k-Ricci tensor and the 2k-Gauss-Bonnet curvature

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Abstract

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.

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