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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 -Einstein (in the sense that
their -Ricci tensor is constant) or have constant -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.Comment: 30 pages; no figure
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