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arXiv · 1208.1801

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

Tiago Caúla·Levi Lopes de Lima·Newton Luis Santos
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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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Tiago Caúla, Levi Lopes de Lima, Newton Luis Santos. 2012-08-09. Deformation and rigidity results for the 2k-Ricci tensor and the 2k-Gauss-Bonnet curvature. https://arxiv.org/abs/1208.1801

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